id	sid	tid	token	lemma	pos
ejpam-4830	1	1	european	european	PROPN
ejpam-4830	1	2	journal	journal	PROPN
ejpam-4830	1	3	of	of	ADP
ejpam-4830	1	4	pure	pure	ADJ
ejpam-4830	1	5	and	and	CCONJ
ejpam-4830	1	6	applied	apply	VERB
ejpam-4830	1	7	mathematics	mathematic	NOUN
ejpam-4830	1	8	vol	vol	NOUN
ejpam-4830	1	9	.	.	PUNCT
ejpam-4830	2	1	16	16	NUM
ejpam-4830	2	2	,	,	PUNCT
ejpam-4830	2	3	no	no	INTJ
ejpam-4830	2	4	.	.	NOUN
ejpam-4830	2	5	3	3	NUM
ejpam-4830	2	6	,	,	PUNCT
ejpam-4830	2	7	2023	2023	NUM
ejpam-4830	2	8	,	,	PUNCT
ejpam-4830	2	9	1830	1830	NUM
ejpam-4830	2	10	-	-	SYM
ejpam-4830	2	11	1847	1847	NUM
ejpam-4830	2	12	issn	issn	VERB
ejpam-4830	2	13	1307	1307	NUM
ejpam-4830	2	14	-	-	SYM
ejpam-4830	2	15	5543	5543	NUM
ejpam-4830	2	16	–	–	PUNCT
ejpam-4830	2	17	ejpam.com	ejpam.com	X
ejpam-4830	2	18	published	publish	VERB
ejpam-4830	2	19	by	by	ADP
ejpam-4830	2	20	new	new	PROPN
ejpam-4830	2	21	york	york	PROPN
ejpam-4830	2	22	business	business	PROPN
ejpam-4830	2	23	global	global	PROPN
ejpam-4830	2	24	british	british	PROPN
ejpam-4830	2	25	put	put	VERB
ejpam-4830	2	26	option	option	NOUN
ejpam-4830	2	27	on	on	ADP
ejpam-4830	2	28	stocks	stock	NOUN
ejpam-4830	2	29	under	under	ADP
ejpam-4830	2	30	regime	regime	NOUN
ejpam-4830	2	31	-	-	PUNCT
ejpam-4830	2	32	switching	switch	VERB
ejpam-4830	2	33	model	model	NOUN
ejpam-4830	2	34	felipe	felipe	PROPN
ejpam-4830	2	35	r.	r.	PROPN
ejpam-4830	2	36	sumalpong	sumalpong	PROPN
ejpam-4830	2	37	,	,	PUNCT
ejpam-4830	2	38	jr.1,∗	jr.1,∗	PROPN
ejpam-4830	2	39	,	,	PUNCT
ejpam-4830	2	40	michael	michael	PROPN
ejpam-4830	2	41	b.	b.	PROPN
ejpam-4830	2	42	frondoza1	frondoza1	PROPN
ejpam-4830	2	43	,	,	PUNCT
ejpam-4830	2	44	noel	noel	PROPN
ejpam-4830	2	45	lito	lito	PROPN
ejpam-4830	2	46	b.	b.	PROPN
ejpam-4830	2	47	sayson3	sayson3	PROPN
ejpam-4830	3	1	1	1	NUM
ejpam-4830	3	2	department	department	NOUN
ejpam-4830	3	3	of	of	ADP
ejpam-4830	3	4	mathematics	mathematic	NOUN
ejpam-4830	3	5	and	and	CCONJ
ejpam-4830	3	6	statistics	statistic	NOUN
ejpam-4830	3	7	,	,	PUNCT
ejpam-4830	3	8	faculty	faculty	NOUN
ejpam-4830	3	9	/	/	SYM
ejpam-4830	3	10	mindanao	mindanao	PROPN
ejpam-4830	3	11	state	state	PROPN
ejpam-4830	3	12	university	university	PROPN
ejpam-4830	3	13	iligan	iligan	PROPN
ejpam-4830	3	14	institute	institute	PROPN
ejpam-4830	3	15	of	of	ADP
ejpam-4830	3	16	technology	technology	PROPN
ejpam-4830	3	17	,	,	PUNCT
ejpam-4830	3	18	iligan	iligan	PROPN
ejpam-4830	3	19	city	city	PROPN
ejpam-4830	3	20	,	,	PUNCT
ejpam-4830	3	21	philippines	philippines	PROPN
ejpam-4830	3	22	2	2	NUM
ejpam-4830	3	23	department	department	NOUN
ejpam-4830	3	24	of	of	ADP
ejpam-4830	3	25	physics	physics	PROPN
ejpam-4830	3	26	,	,	PUNCT
ejpam-4830	3	27	faculty	faculty	NOUN
ejpam-4830	3	28	/	/	SYM
ejpam-4830	3	29	mindanao	mindanao	PROPN
ejpam-4830	3	30	state	state	PROPN
ejpam-4830	3	31	university	university	PROPN
ejpam-4830	3	32	iligan	iligan	PROPN
ejpam-4830	3	33	institute	institute	PROPN
ejpam-4830	3	34	of	of	ADP
ejpam-4830	3	35	technology	technology	PROPN
ejpam-4830	3	36	,	,	PUNCT
ejpam-4830	3	37	iligan	iligan	PROPN
ejpam-4830	3	38	city	city	PROPN
ejpam-4830	3	39	,	,	PUNCT
ejpam-4830	3	40	philippines	philippine	NOUN
ejpam-4830	3	41	abstract	abstract	ADJ
ejpam-4830	3	42	.	.	PUNCT
ejpam-4830	4	1	in	in	ADP
ejpam-4830	4	2	a	a	DET
ejpam-4830	4	3	plain	plain	ADJ
ejpam-4830	4	4	vanilla	vanilla	NOUN
ejpam-4830	4	5	option	option	NOUN
ejpam-4830	4	6	,	,	PUNCT
ejpam-4830	4	7	its	its	PRON
ejpam-4830	4	8	holder	holder	NOUN
ejpam-4830	4	9	is	be	AUX
ejpam-4830	4	10	given	give	VERB
ejpam-4830	4	11	the	the	DET
ejpam-4830	4	12	right	right	NOUN
ejpam-4830	4	13	,	,	PUNCT
ejpam-4830	4	14	but	but	CCONJ
ejpam-4830	4	15	not	not	PART
ejpam-4830	4	16	the	the	DET
ejpam-4830	4	17	obligation	obligation	NOUN
ejpam-4830	4	18	,	,	PUNCT
ejpam-4830	4	19	to	to	PART
ejpam-4830	4	20	buy	buy	VERB
ejpam-4830	4	21	or	or	CCONJ
ejpam-4830	4	22	sell	sell	VERB
ejpam-4830	4	23	the	the	DET
ejpam-4830	4	24	underlying	underlie	VERB
ejpam-4830	4	25	stock	stock	NOUN
ejpam-4830	4	26	at	at	ADP
ejpam-4830	4	27	a	a	DET
ejpam-4830	4	28	specified	specified	ADJ
ejpam-4830	4	29	price	price	NOUN
ejpam-4830	4	30	(	(	PUNCT
ejpam-4830	4	31	strike	strike	NOUN
ejpam-4830	4	32	price	price	NOUN
ejpam-4830	4	33	)	)	PUNCT
ejpam-4830	4	34	at	at	ADP
ejpam-4830	4	35	a	a	DET
ejpam-4830	4	36	predetermined	predetermine	VERB
ejpam-4830	4	37	date	date	NOUN
ejpam-4830	4	38	.	.	PUNCT
ejpam-4830	5	1	if	if	SCONJ
ejpam-4830	5	2	the	the	DET
ejpam-4830	5	3	exercise	exercise	NOUN
ejpam-4830	5	4	date	date	NOUN
ejpam-4830	5	5	is	be	AUX
ejpam-4830	5	6	at	at	ADP
ejpam-4830	5	7	maturity	maturity	NOUN
ejpam-4830	5	8	,	,	PUNCT
ejpam-4830	5	9	the	the	DET
ejpam-4830	5	10	option	option	NOUN
ejpam-4830	5	11	is	be	AUX
ejpam-4830	5	12	called	call	VERB
ejpam-4830	5	13	a	a	DET
ejpam-4830	5	14	european	european	NOUN
ejpam-4830	5	15	;	;	PUNCT
ejpam-4830	5	16	if	if	SCONJ
ejpam-4830	5	17	the	the	DET
ejpam-4830	5	18	option	option	NOUN
ejpam-4830	5	19	is	be	AUX
ejpam-4830	5	20	exercised	exercise	VERB
ejpam-4830	5	21	anytime	anytime	ADV
ejpam-4830	5	22	prior	prior	ADV
ejpam-4830	5	23	to	to	ADP
ejpam-4830	5	24	maturity	maturity	NOUN
ejpam-4830	5	25	,	,	PUNCT
ejpam-4830	5	26	it	it	PRON
ejpam-4830	5	27	is	be	AUX
ejpam-4830	5	28	called	call	VERB
ejpam-4830	5	29	an	an	DET
ejpam-4830	5	30	american	american	PROPN
ejpam-4830	5	31	.	.	PUNCT
ejpam-4830	6	1	in	in	ADP
ejpam-4830	6	2	a	a	DET
ejpam-4830	6	3	british	british	ADJ
ejpam-4830	6	4	option	option	NOUN
ejpam-4830	6	5	,	,	PUNCT
ejpam-4830	6	6	the	the	DET
ejpam-4830	6	7	holder	holder	NOUN
ejpam-4830	6	8	can	can	AUX
ejpam-4830	6	9	enjoy	enjoy	VERB
ejpam-4830	6	10	the	the	DET
ejpam-4830	6	11	early	early	ADJ
ejpam-4830	6	12	exercise	exercise	NOUN
ejpam-4830	6	13	feature	feature	NOUN
ejpam-4830	6	14	of	of	ADP
ejpam-4830	6	15	american	american	ADJ
ejpam-4830	6	16	option	option	NOUN
ejpam-4830	6	17	whereupon	whereupon	ADV
ejpam-4830	6	18	his	his	PRON
ejpam-4830	6	19	payoff	payoff	NOUN
ejpam-4830	6	20	is	be	AUX
ejpam-4830	6	21	the	the	DET
ejpam-4830	6	22	‘	'	PUNCT
ejpam-4830	6	23	best	good	ADJ
ejpam-4830	6	24	prediction	prediction	NOUN
ejpam-4830	6	25	’	'	PUNCT
ejpam-4830	6	26	of	of	ADP
ejpam-4830	6	27	the	the	DET
ejpam-4830	6	28	european	european	PROPN
ejpam-4830	6	29	payoff	payoff	NOUN
ejpam-4830	6	30	given	give	VERB
ejpam-4830	6	31	all	all	DET
ejpam-4830	6	32	the	the	DET
ejpam-4830	6	33	information	information	NOUN
ejpam-4830	6	34	up	up	ADP
ejpam-4830	6	35	to	to	PART
ejpam-4830	6	36	exercise	exercise	VERB
ejpam-4830	6	37	date	date	NOUN
ejpam-4830	6	38	under	under	ADP
ejpam-4830	6	39	the	the	DET
ejpam-4830	6	40	hypothesis	hypothesis	NOUN
ejpam-4830	6	41	that	that	PRON
ejpam-4830	6	42	the	the	DET
ejpam-4830	6	43	true	true	ADJ
ejpam-4830	6	44	drift	drift	NOUN
ejpam-4830	6	45	of	of	ADP
ejpam-4830	6	46	the	the	DET
ejpam-4830	6	47	stock	stock	NOUN
ejpam-4830	6	48	equals	equal	VERB
ejpam-4830	6	49	a	a	DET
ejpam-4830	6	50	specified	specified	ADJ
ejpam-4830	6	51	contract	contract	NOUN
ejpam-4830	6	52	drift	drift	NOUN
ejpam-4830	6	53	.	.	PUNCT
ejpam-4830	7	1	in	in	ADP
ejpam-4830	7	2	this	this	DET
ejpam-4830	7	3	paper	paper	NOUN
ejpam-4830	7	4	,	,	PUNCT
ejpam-4830	7	5	in	in	ADP
ejpam-4830	7	6	contrast	contrast	NOUN
ejpam-4830	7	7	to	to	ADP
ejpam-4830	7	8	the	the	DET
ejpam-4830	7	9	constant	constant	ADJ
ejpam-4830	7	10	interest	interest	NOUN
ejpam-4830	7	11	rate	rate	NOUN
ejpam-4830	7	12	and	and	CCONJ
ejpam-4830	7	13	constant	constant	ADJ
ejpam-4830	7	14	volatility	volatility	NOUN
ejpam-4830	7	15	assumptions	assumption	NOUN
ejpam-4830	7	16	,	,	PUNCT
ejpam-4830	7	17	we	we	PRON
ejpam-4830	7	18	consider	consider	VERB
ejpam-4830	7	19	the	the	DET
ejpam-4830	7	20	british	british	ADJ
ejpam-4830	7	21	option	option	NOUN
ejpam-4830	7	22	by	by	ADP
ejpam-4830	7	23	assuming	assume	VERB
ejpam-4830	7	24	that	that	SCONJ
ejpam-4830	7	25	the	the	DET
ejpam-4830	7	26	economic	economic	ADJ
ejpam-4830	7	27	state	state	NOUN
ejpam-4830	7	28	of	of	ADP
ejpam-4830	7	29	the	the	DET
ejpam-4830	7	30	world	world	NOUN
ejpam-4830	7	31	is	be	AUX
ejpam-4830	7	32	described	describe	VERB
ejpam-4830	7	33	by	by	ADP
ejpam-4830	7	34	a	a	DET
ejpam-4830	7	35	finite	finite	ADJ
ejpam-4830	7	36	state	state	NOUN
ejpam-4830	7	37	continuous	continuous	ADJ
ejpam-4830	7	38	-	-	PUNCT
ejpam-4830	7	39	time	time	NOUN
ejpam-4830	7	40	markov	markov	NOUN
ejpam-4830	7	41	chain	chain	NOUN
ejpam-4830	7	42	.	.	PUNCT
ejpam-4830	8	1	also	also	ADV
ejpam-4830	8	2	,	,	PUNCT
ejpam-4830	8	3	we	we	PRON
ejpam-4830	8	4	provide	provide	VERB
ejpam-4830	8	5	a	a	DET
ejpam-4830	8	6	solution	solution	NOUN
ejpam-4830	8	7	to	to	ADP
ejpam-4830	8	8	a	a	DET
ejpam-4830	8	9	free	free	ADJ
ejpam-4830	8	10	boundary	boundary	ADJ
ejpam-4830	8	11	problem	problem	NOUN
ejpam-4830	8	12	by	by	ADP
ejpam-4830	8	13	using	use	VERB
ejpam-4830	8	14	pde	pde	NOUN
ejpam-4830	8	15	arguments	argument	NOUN
ejpam-4830	8	16	.	.	PUNCT
ejpam-4830	9	1	however	however	ADV
ejpam-4830	9	2	,	,	PUNCT
ejpam-4830	9	3	closed	close	VERB
ejpam-4830	9	4	form	form	NOUN
ejpam-4830	9	5	expression	expression	NOUN
ejpam-4830	9	6	for	for	ADP
ejpam-4830	9	7	the	the	DET
ejpam-4830	9	8	arbitrage	arbitrage	NOUN
ejpam-4830	9	9	-	-	PUNCT
ejpam-4830	9	10	free	free	ADJ
ejpam-4830	9	11	price	price	NOUN
ejpam-4830	9	12	are	be	AUX
ejpam-4830	9	13	not	not	PART
ejpam-4830	9	14	available	available	ADJ
ejpam-4830	9	15	in	in	ADP
ejpam-4830	9	16	our	our	PRON
ejpam-4830	9	17	setting	setting	NOUN
ejpam-4830	9	18	.	.	PUNCT
ejpam-4830	10	1	2020	2020	NUM
ejpam-4830	10	2	mathematics	mathematic	NOUN
ejpam-4830	10	3	subject	subject	NOUN
ejpam-4830	10	4	classifications	classification	NOUN
ejpam-4830	10	5	:	:	PUNCT
ejpam-4830	10	6	62p05	62p05	NUM
ejpam-4830	10	7	,	,	PUNCT
ejpam-4830	10	8	97m30	97m30	NUM
ejpam-4830	10	9	key	key	ADJ
ejpam-4830	10	10	words	word	NOUN
ejpam-4830	10	11	and	and	CCONJ
ejpam-4830	10	12	phrases	phrase	NOUN
ejpam-4830	10	13	:	:	PUNCT
ejpam-4830	10	14	british	british	ADJ
ejpam-4830	10	15	put	put	VERB
ejpam-4830	10	16	option	option	NOUN
ejpam-4830	10	17	,	,	PUNCT
ejpam-4830	10	18	american	american	ADJ
ejpam-4830	10	19	put	put	NOUN
ejpam-4830	10	20	option	option	NOUN
ejpam-4830	10	21	,	,	PUNCT
ejpam-4830	10	22	european	european	ADJ
ejpam-4830	10	23	put	put	NOUN
ejpam-4830	10	24	option	option	NOUN
ejpam-4830	10	25	,	,	PUNCT
ejpam-4830	10	26	arbitrage	arbitrage	NOUN
ejpam-4830	10	27	-	-	PUNCT
ejpam-4830	10	28	free	free	ADJ
ejpam-4830	10	29	price	price	NOUN
ejpam-4830	10	30	,	,	PUNCT
ejpam-4830	10	31	rational	rational	ADJ
ejpam-4830	10	32	exercise	exercise	NOUN
ejpam-4830	10	33	boundary	boundary	NOUN
ejpam-4830	10	34	,	,	PUNCT
ejpam-4830	10	35	geometric	geometric	ADJ
ejpam-4830	10	36	brownian	brownian	ADJ
ejpam-4830	10	37	motion	motion	NOUN
ejpam-4830	10	38	,	,	PUNCT
ejpam-4830	10	39	optimal	optimal	ADJ
ejpam-4830	10	40	stopping	stopping	NOUN
ejpam-4830	10	41	time	time	NOUN
ejpam-4830	10	42	,	,	PUNCT
ejpam-4830	10	43	free	free	ADJ
ejpam-4830	10	44	boundary	boundary	ADJ
ejpam-4830	10	45	problem	problem	NOUN
ejpam-4830	10	46	,	,	PUNCT
ejpam-4830	10	47	regime	regime	NOUN
ejpam-4830	10	48	-	-	PUNCT
ejpam-4830	10	49	switching	switch	VERB
ejpam-4830	10	50	1	1	NUM
ejpam-4830	10	51	.	.	PUNCT
ejpam-4830	11	1	introduction	introduction	NOUN
ejpam-4830	11	2	plain	plain	ADJ
ejpam-4830	11	3	vanilla	vanilla	NOUN
ejpam-4830	11	4	options	option	NOUN
ejpam-4830	11	5	such	such	ADJ
ejpam-4830	11	6	as	as	ADP
ejpam-4830	11	7	european	european	ADJ
ejpam-4830	11	8	options	option	NOUN
ejpam-4830	11	9	and	and	CCONJ
ejpam-4830	11	10	american	american	ADJ
ejpam-4830	11	11	options	option	NOUN
ejpam-4830	11	12	are	be	AUX
ejpam-4830	11	13	widely	widely	ADV
ejpam-4830	11	14	used	use	VERB
ejpam-4830	11	15	in	in	ADP
ejpam-4830	11	16	the	the	DET
ejpam-4830	11	17	market	market	NOUN
ejpam-4830	11	18	and	and	CCONJ
ejpam-4830	11	19	their	their	PRON
ejpam-4830	11	20	pricing	pricing	NOUN
ejpam-4830	11	21	mechanisms	mechanism	NOUN
ejpam-4830	11	22	are	be	AUX
ejpam-4830	11	23	well	well	ADV
ejpam-4830	11	24	studied	study	VERB
ejpam-4830	11	25	.	.	PUNCT
ejpam-4830	12	1	an	an	DET
ejpam-4830	12	2	option	option	NOUN
ejpam-4830	12	3	gives	give	VERB
ejpam-4830	12	4	the	the	DET
ejpam-4830	12	5	holder	holder	NOUN
ejpam-4830	12	6	the	the	DET
ejpam-4830	12	7	right	right	NOUN
ejpam-4830	12	8	,	,	PUNCT
ejpam-4830	12	9	but	but	CCONJ
ejpam-4830	12	10	not	not	PART
ejpam-4830	12	11	the	the	DET
ejpam-4830	12	12	obligation	obligation	NOUN
ejpam-4830	12	13	,	,	PUNCT
ejpam-4830	12	14	to	to	PART
ejpam-4830	12	15	buy	buy	VERB
ejpam-4830	12	16	or	or	CCONJ
ejpam-4830	12	17	sell	sell	VERB
ejpam-4830	12	18	an	an	DET
ejpam-4830	12	19	underlying	underlie	VERB
ejpam-4830	12	20	asset	asset	NOUN
ejpam-4830	12	21	for	for	ADP
ejpam-4830	12	22	a	a	DET
ejpam-4830	12	23	specified	specify	VERB
ejpam-4830	12	24	price	price	NOUN
ejpam-4830	12	25	,	,	PUNCT
ejpam-4830	12	26	called	call	VERB
ejpam-4830	12	27	strike	strike	NOUN
ejpam-4830	12	28	price	price	NOUN
ejpam-4830	12	29	,	,	PUNCT
ejpam-4830	12	30	on	on	ADV
ejpam-4830	12	31	or	or	CCONJ
ejpam-4830	12	32	before	before	ADP
ejpam-4830	12	33	a	a	DET
ejpam-4830	12	34	specified	specify	VERB
ejpam-4830	12	35	future	future	ADJ
ejpam-4830	12	36	date	date	NOUN
ejpam-4830	12	37	,	,	PUNCT
ejpam-4830	12	38	called	call	VERB
ejpam-4830	12	39	maturity	maturity	NOUN
ejpam-4830	12	40	date	date	NOUN
ejpam-4830	12	41	or	or	CCONJ
ejpam-4830	12	42	expiration	expiration	NOUN
ejpam-4830	12	43	date	date	NOUN
ejpam-4830	12	44	.	.	PUNCT
ejpam-4830	13	1	the	the	DET
ejpam-4830	13	2	option	option	NOUN
ejpam-4830	13	3	is	be	AUX
ejpam-4830	13	4	european	european	ADJ
ejpam-4830	13	5	if	if	SCONJ
ejpam-4830	13	6	the	the	DET
ejpam-4830	13	7	holder	holder	NOUN
ejpam-4830	13	8	can	can	AUX
ejpam-4830	13	9	exercise	exercise	VERB
ejpam-4830	13	10	it	it	PRON
ejpam-4830	13	11	only	only	ADV
ejpam-4830	13	12	at	at	ADP
ejpam-4830	13	13	expiration	expiration	NOUN
ejpam-4830	13	14	date	date	NOUN
ejpam-4830	13	15	;	;	PUNCT
ejpam-4830	13	16	it	it	PRON
ejpam-4830	13	17	is	be	AUX
ejpam-4830	13	18	american	american	ADJ
ejpam-4830	13	19	if	if	SCONJ
ejpam-4830	13	20	the	the	DET
ejpam-4830	13	21	option	option	NOUN
ejpam-4830	13	22	can	can	AUX
ejpam-4830	13	23	be	be	AUX
ejpam-4830	13	24	exercised	exercise	VERB
ejpam-4830	13	25	anytime	anytime	ADV
ejpam-4830	13	26	even	even	ADV
ejpam-4830	13	27	prior	prior	ADV
ejpam-4830	13	28	to	to	ADP
ejpam-4830	13	29	the	the	DET
ejpam-4830	13	30	expiration	expiration	NOUN
ejpam-4830	13	31	date	date	NOUN
ejpam-4830	13	32	.	.	PUNCT
ejpam-4830	14	1	∗corresponding	∗corresponde	VERB
ejpam-4830	14	2	author	author	NOUN
ejpam-4830	14	3	.	.	PUNCT
ejpam-4830	15	1	doi	doi	NOUN
ejpam-4830	15	2	:	:	PUNCT
ejpam-4830	15	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4830	https://doi.org/10.29020/nybg.ejpam.v16i3.4830	NOUN
ejpam-4830	15	4	email	email	NOUN
ejpam-4830	15	5	addresses	address	VERB
ejpam-4830	15	6	:	:	PUNCT
ejpam-4830	15	7	felipejr.sumalpong@g.msuiit.edu.ph	felipejr.sumalpong@g.msuiit.edu.ph	PROPN
ejpam-4830	15	8	(	(	PUNCT
ejpam-4830	15	9	f.jr	f.jr	PROPN
ejpam-4830	15	10	.	.	PROPN
ejpam-4830	15	11	sumalpong	sumalpong	PROPN
ejpam-4830	15	12	)	)	PUNCT
ejpam-4830	15	13	,	,	PUNCT
ejpam-4830	15	14	michael.frondoza@g.msuiit.edu.ph	michael.frondoza@g.msuiit.edu.ph	PROPN
ejpam-4830	15	15	(	(	PUNCT
ejpam-4830	15	16	m.	m.	NOUN
ejpam-4830	15	17	frondoza	frondoza	PROPN
ejpam-4830	15	18	)	)	PUNCT
ejpam-4830	15	19	,	,	PUNCT
ejpam-4830	15	20	noellito.sayson@g.msuiit.edu.ph	noellito.sayson@g.msuiit.edu.ph	PROPN
ejpam-4830	15	21	(	(	PUNCT
ejpam-4830	15	22	n.l	n.l	PROPN
ejpam-4830	15	23	.	.	PROPN
ejpam-4830	15	24	b.	b.	PROPN
ejpam-4830	15	25	sayson	sayson	PROPN
ejpam-4830	15	26	)	)	PUNCT
ejpam-4830	15	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4830	15	28	1830	1830	NUM
ejpam-4830	16	1	©	©	ADP
ejpam-4830	16	2	2023	2023	NUM
ejpam-4830	16	3	ejpam	ejpam	NOUN
ejpam-4830	16	4	all	all	DET
ejpam-4830	16	5	rights	right	NOUN
ejpam-4830	16	6	reserved	reserve	VERB
ejpam-4830	16	7	.	.	PUNCT
ejpam-4830	17	1	f.	f.	PROPN
ejpam-4830	17	2	sumalpong	sumalpong	PROPN
ejpam-4830	17	3	,	,	PUNCT
ejpam-4830	17	4	m.	m.	PROPN
ejpam-4830	17	5	frondoza	frondoza	PROPN
ejpam-4830	17	6	,	,	PUNCT
ejpam-4830	17	7	n.l	n.l	PROPN
ejpam-4830	17	8	.	.	PROPN
ejpam-4830	17	9	sayson	sayson	PROPN
ejpam-4830	17	10	/	/	SYM
ejpam-4830	17	11	eur	eur	PROPN
ejpam-4830	17	12	.	.	PUNCT
ejpam-4830	18	1	j.	j.	PROPN
ejpam-4830	18	2	pure	pure	PROPN
ejpam-4830	18	3	appl	appl	PROPN
ejpam-4830	18	4	.	.	PROPN
ejpam-4830	18	5	math	math	PROPN
ejpam-4830	18	6	,	,	PUNCT
ejpam-4830	18	7	16	16	NUM
ejpam-4830	18	8	(	(	PUNCT
ejpam-4830	18	9	3	3	NUM
ejpam-4830	18	10	)	)	PUNCT
ejpam-4830	18	11	(	(	PUNCT
ejpam-4830	18	12	2023	2023	NUM
ejpam-4830	18	13	)	)	PUNCT
ejpam-4830	18	14	,	,	PUNCT
ejpam-4830	18	15	1830	1830	NUM
ejpam-4830	18	16	-	-	SYM
ejpam-4830	18	17	1847	1847	NUM
ejpam-4830	18	18	1831	1831	NUM
ejpam-4830	18	19	one	one	NUM
ejpam-4830	18	20	of	of	ADP
ejpam-4830	18	21	the	the	DET
ejpam-4830	18	22	pricing	pricing	NOUN
ejpam-4830	18	23	mechanisms	mechanism	NOUN
ejpam-4830	18	24	for	for	ADP
ejpam-4830	18	25	european	european	ADJ
ejpam-4830	18	26	option	option	NOUN
ejpam-4830	18	27	is	be	AUX
ejpam-4830	18	28	provided	provide	VERB
ejpam-4830	18	29	by	by	ADP
ejpam-4830	18	30	the	the	DET
ejpam-4830	18	31	well	well	ADV
ejpam-4830	18	32	-	-	PUNCT
ejpam-4830	18	33	known	know	VERB
ejpam-4830	18	34	black	black	ADJ
ejpam-4830	18	35	-	-	PUNCT
ejpam-4830	18	36	scholes	schole	NOUN
ejpam-4830	18	37	-	-	PUNCT
ejpam-4830	18	38	merton	merton	NOUN
ejpam-4830	18	39	formula	formula	NOUN
ejpam-4830	18	40	.	.	PUNCT
ejpam-4830	19	1	this	this	DET
ejpam-4830	19	2	mathematical	mathematical	ADJ
ejpam-4830	19	3	model	model	NOUN
ejpam-4830	19	4	assumes	assume	VERB
ejpam-4830	19	5	,	,	PUNCT
ejpam-4830	19	6	among	among	ADP
ejpam-4830	19	7	other	other	ADJ
ejpam-4830	19	8	things	thing	NOUN
ejpam-4830	19	9	,	,	PUNCT
ejpam-4830	19	10	the	the	DET
ejpam-4830	19	11	absence	absence	NOUN
ejpam-4830	19	12	of	of	ADP
ejpam-4830	19	13	arbitrage	arbitrage	NOUN
ejpam-4830	19	14	opportunities	opportunity	NOUN
ejpam-4830	19	15	and	and	CCONJ
ejpam-4830	19	16	that	that	SCONJ
ejpam-4830	19	17	lending	lending	NOUN
ejpam-4830	19	18	and	and	CCONJ
ejpam-4830	19	19	borrowing	borrowing	NOUN
ejpam-4830	19	20	are	be	AUX
ejpam-4830	19	21	possible	possible	ADJ
ejpam-4830	19	22	at	at	ADP
ejpam-4830	19	23	the	the	DET
ejpam-4830	19	24	same	same	ADJ
ejpam-4830	19	25	risk	risk	NOUN
ejpam-4830	19	26	-	-	PUNCT
ejpam-4830	19	27	free	free	ADJ
ejpam-4830	19	28	rate	rate	NOUN
ejpam-4830	19	29	.	.	PUNCT
ejpam-4830	20	1	such	such	ADJ
ejpam-4830	20	2	method	method	NOUN
ejpam-4830	20	3	falls	fall	VERB
ejpam-4830	20	4	within	within	ADP
ejpam-4830	20	5	the	the	DET
ejpam-4830	20	6	so	so	ADV
ejpam-4830	20	7	-	-	PUNCT
ejpam-4830	20	8	called	call	VERB
ejpam-4830	20	9	risk	risk	NOUN
ejpam-4830	20	10	-	-	PUNCT
ejpam-4830	20	11	neutral	neutral	ADJ
ejpam-4830	20	12	pricing	pricing	NOUN
ejpam-4830	20	13	framework	framework	NOUN
ejpam-4830	20	14	.	.	PUNCT
ejpam-4830	21	1	in	in	ADP
ejpam-4830	21	2	[	[	X
ejpam-4830	21	3	5	5	NUM
ejpam-4830	21	4	]	]	PUNCT
ejpam-4830	21	5	,	,	PUNCT
ejpam-4830	21	6	g.	g.	PROPN
ejpam-4830	21	7	peskir	peskir	PROPN
ejpam-4830	21	8	and	and	CCONJ
ejpam-4830	21	9	f.	f.	PROPN
ejpam-4830	21	10	samee	samee	PROPN
ejpam-4830	21	11	introduced	introduce	VERB
ejpam-4830	21	12	a	a	DET
ejpam-4830	21	13	new	new	ADJ
ejpam-4830	21	14	type	type	NOUN
ejpam-4830	21	15	of	of	ADP
ejpam-4830	21	16	option	option	NOUN
ejpam-4830	21	17	,	,	PUNCT
ejpam-4830	21	18	called	call	VERB
ejpam-4830	21	19	british	british	ADJ
ejpam-4830	21	20	option	option	NOUN
ejpam-4830	21	21	,	,	PUNCT
ejpam-4830	21	22	which	which	PRON
ejpam-4830	21	23	is	be	AUX
ejpam-4830	21	24	american	american	ADJ
ejpam-4830	21	25	in	in	ADP
ejpam-4830	21	26	nature	nature	NOUN
ejpam-4830	21	27	because	because	SCONJ
ejpam-4830	21	28	it	it	PRON
ejpam-4830	21	29	can	can	AUX
ejpam-4830	21	30	be	be	AUX
ejpam-4830	21	31	exercised	exercise	VERB
ejpam-4830	21	32	prior	prior	ADV
ejpam-4830	21	33	to	to	ADP
ejpam-4830	21	34	maturity	maturity	NOUN
ejpam-4830	21	35	but	but	CCONJ
ejpam-4830	21	36	with	with	ADP
ejpam-4830	21	37	european	european	PROPN
ejpam-4830	21	38	payoff	payoff	PROPN
ejpam-4830	21	39	.	.	PUNCT
ejpam-4830	22	1	the	the	DET
ejpam-4830	22	2	motivation	motivation	NOUN
ejpam-4830	22	3	for	for	ADP
ejpam-4830	22	4	this	this	DET
ejpam-4830	22	5	new	new	ADJ
ejpam-4830	22	6	financial	financial	ADJ
ejpam-4830	22	7	product	product	NOUN
ejpam-4830	22	8	stems	stem	VERB
ejpam-4830	22	9	from	from	ADP
ejpam-4830	22	10	the	the	DET
ejpam-4830	22	11	disparity	disparity	NOUN
ejpam-4830	22	12	between	between	ADP
ejpam-4830	22	13	the	the	DET
ejpam-4830	22	14	expected	expect	VERB
ejpam-4830	22	15	value	value	NOUN
ejpam-4830	22	16	of	of	ADP
ejpam-4830	22	17	the	the	DET
ejpam-4830	22	18	option	option	NOUN
ejpam-4830	22	19	buyer	buyer	NOUN
ejpam-4830	22	20	’s	’s	PART
ejpam-4830	22	21	investment	investment	NOUN
ejpam-4830	22	22	,	,	PUNCT
ejpam-4830	22	23	in	in	ADP
ejpam-4830	22	24	the	the	DET
ejpam-4830	22	25	form	form	NOUN
ejpam-4830	22	26	of	of	ADP
ejpam-4830	22	27	premium	premium	NOUN
ejpam-4830	22	28	paid	pay	VERB
ejpam-4830	22	29	,	,	PUNCT
ejpam-4830	22	30	and	and	CCONJ
ejpam-4830	22	31	the	the	DET
ejpam-4830	22	32	expected	expect	VERB
ejpam-4830	22	33	value	value	NOUN
ejpam-4830	22	34	of	of	ADP
ejpam-4830	22	35	his	his	PRON
ejpam-4830	22	36	payoff	payoff	NOUN
ejpam-4830	22	37	when	when	SCONJ
ejpam-4830	22	38	the	the	DET
ejpam-4830	22	39	actual	actual	ADJ
ejpam-4830	22	40	drift	drift	NOUN
ejpam-4830	22	41	rate	rate	NOUN
ejpam-4830	22	42	of	of	ADP
ejpam-4830	22	43	the	the	DET
ejpam-4830	22	44	underlying	underlie	VERB
ejpam-4830	22	45	stock	stock	NOUN
ejpam-4830	22	46	price	price	NOUN
ejpam-4830	22	47	deviates	deviate	VERB
ejpam-4830	22	48	from	from	ADP
ejpam-4830	22	49	the	the	DET
ejpam-4830	22	50	risk	risk	NOUN
ejpam-4830	22	51	-	-	PUNCT
ejpam-4830	22	52	free	free	ADJ
ejpam-4830	22	53	rate	rate	NOUN
ejpam-4830	22	54	.	.	PUNCT
ejpam-4830	23	1	an	an	DET
ejpam-4830	23	2	added	add	VERB
ejpam-4830	23	3	feature	feature	NOUN
ejpam-4830	23	4	is	be	AUX
ejpam-4830	23	5	built	build	VERB
ejpam-4830	23	6	into	into	ADP
ejpam-4830	23	7	this	this	DET
ejpam-4830	23	8	instrument	instrument	NOUN
ejpam-4830	23	9	which	which	PRON
ejpam-4830	23	10	aim	aim	VERB
ejpam-4830	23	11	at	at	ADP
ejpam-4830	23	12	both	both	PRON
ejpam-4830	23	13	providing	provide	VERB
ejpam-4830	23	14	protection	protection	NOUN
ejpam-4830	23	15	against	against	ADP
ejpam-4830	23	16	unfavourable	unfavourable	ADJ
ejpam-4830	23	17	price	price	NOUN
ejpam-4830	23	18	movements	movement	NOUN
ejpam-4830	23	19	as	as	ADV
ejpam-4830	23	20	well	well	ADV
ejpam-4830	23	21	as	as	ADP
ejpam-4830	23	22	securing	secure	VERB
ejpam-4830	23	23	higher	high	ADJ
ejpam-4830	23	24	returns	return	NOUN
ejpam-4830	23	25	when	when	SCONJ
ejpam-4830	23	26	these	these	DET
ejpam-4830	23	27	movements	movement	NOUN
ejpam-4830	23	28	are	be	AUX
ejpam-4830	23	29	favourable	favourable	ADJ
ejpam-4830	23	30	[	[	X
ejpam-4830	23	31	5	5	NUM
ejpam-4830	23	32	]	]	PUNCT
ejpam-4830	23	33	.	.	PUNCT
ejpam-4830	24	1	the	the	DET
ejpam-4830	24	2	derivation	derivation	NOUN
ejpam-4830	24	3	of	of	ADP
ejpam-4830	24	4	the	the	DET
ejpam-4830	24	5	british	british	ADJ
ejpam-4830	24	6	option	option	NOUN
ejpam-4830	24	7	price	price	NOUN
ejpam-4830	24	8	in	in	ADP
ejpam-4830	24	9	[	[	X
ejpam-4830	24	10	5	5	NUM
ejpam-4830	24	11	]	]	PUNCT
ejpam-4830	24	12	assumes	assume	VERB
ejpam-4830	24	13	the	the	DET
ejpam-4830	24	14	usual	usual	ADJ
ejpam-4830	24	15	model	model	NOUN
ejpam-4830	24	16	as	as	ADP
ejpam-4830	24	17	in	in	ADP
ejpam-4830	24	18	the	the	DET
ejpam-4830	24	19	black	black	ADJ
ejpam-4830	24	20	-	-	PUNCT
ejpam-4830	24	21	scholes	schole	NOUN
ejpam-4830	24	22	-	-	PUNCT
ejpam-4830	24	23	merton	merton	NOUN
ejpam-4830	24	24	formula	formula	NOUN
ejpam-4830	24	25	:	:	PUNCT
ejpam-4830	24	26	a	a	DET
ejpam-4830	24	27	geometric	geometric	ADJ
ejpam-4830	24	28	brownian	brownian	ADJ
ejpam-4830	24	29	motion	motion	NOUN
ejpam-4830	24	30	for	for	ADP
ejpam-4830	24	31	the	the	DET
ejpam-4830	24	32	dynamics	dynamic	NOUN
ejpam-4830	24	33	of	of	ADP
ejpam-4830	24	34	the	the	DET
ejpam-4830	24	35	underlying	underlie	VERB
ejpam-4830	24	36	stock	stock	NOUN
ejpam-4830	24	37	,	,	PUNCT
ejpam-4830	24	38	a	a	DET
ejpam-4830	24	39	constant	constant	ADJ
ejpam-4830	24	40	risk	risk	NOUN
ejpam-4830	24	41	-	-	PUNCT
ejpam-4830	24	42	free	free	ADJ
ejpam-4830	24	43	interest	interest	NOUN
ejpam-4830	24	44	rate	rate	NOUN
ejpam-4830	24	45	and	and	CCONJ
ejpam-4830	24	46	a	a	DET
ejpam-4830	24	47	constant	constant	ADJ
ejpam-4830	24	48	volatility	volatility	NOUN
ejpam-4830	24	49	.	.	PUNCT
ejpam-4830	25	1	in	in	ADP
ejpam-4830	25	2	[	[	X
ejpam-4830	25	3	2	2	NUM
ejpam-4830	25	4	]	]	PUNCT
ejpam-4830	25	5	,	,	PUNCT
ejpam-4830	25	6	yao	yao	PROPN
ejpam-4830	25	7	,	,	PUNCT
ejpam-4830	25	8	zhang	zhang	PROPN
ejpam-4830	25	9	and	and	CCONJ
ejpam-4830	25	10	zhou	zhou	PROPN
ejpam-4830	25	11	priced	price	VERB
ejpam-4830	25	12	the	the	DET
ejpam-4830	25	13	european	european	ADJ
ejpam-4830	25	14	options	option	NOUN
ejpam-4830	25	15	in	in	ADP
ejpam-4830	25	16	continuous	continuous	ADJ
ejpam-4830	25	17	-	-	PUNCT
ejpam-4830	25	18	time	time	NOUN
ejpam-4830	25	19	regime	regime	NOUN
ejpam-4830	25	20	-	-	PUNCT
ejpam-4830	25	21	switching	switching	NOUN
ejpam-4830	25	22	via	via	ADP
ejpam-4830	25	23	a	a	DET
ejpam-4830	25	24	recursive	recursive	ADJ
ejpam-4830	25	25	algorithm	algorithm	NOUN
ejpam-4830	25	26	.	.	PUNCT
ejpam-4830	26	1	this	this	DET
ejpam-4830	26	2	paper	paper	NOUN
ejpam-4830	26	3	aims	aim	VERB
ejpam-4830	26	4	to	to	PART
ejpam-4830	26	5	extend	extend	VERB
ejpam-4830	26	6	the	the	DET
ejpam-4830	26	7	result	result	NOUN
ejpam-4830	26	8	in	in	ADP
ejpam-4830	26	9	[	[	X
ejpam-4830	26	10	5	5	NUM
ejpam-4830	26	11	]	]	PUNCT
ejpam-4830	26	12	by	by	ADP
ejpam-4830	26	13	assuming	assume	VERB
ejpam-4830	26	14	that	that	SCONJ
ejpam-4830	26	15	the	the	DET
ejpam-4830	26	16	economic	economic	ADJ
ejpam-4830	26	17	state	state	NOUN
ejpam-4830	26	18	of	of	ADP
ejpam-4830	26	19	the	the	DET
ejpam-4830	26	20	world	world	NOUN
ejpam-4830	26	21	is	be	AUX
ejpam-4830	26	22	described	describe	VERB
ejpam-4830	26	23	by	by	ADP
ejpam-4830	26	24	a	a	DET
ejpam-4830	26	25	finite	finite	ADJ
ejpam-4830	26	26	state	state	NOUN
ejpam-4830	26	27	continuous	continuous	ADJ
ejpam-4830	26	28	-	-	PUNCT
ejpam-4830	26	29	time	time	NOUN
ejpam-4830	26	30	markov	markov	NOUN
ejpam-4830	26	31	chain	chain	NOUN
ejpam-4830	26	32	.	.	PUNCT
ejpam-4830	27	1	the	the	DET
ejpam-4830	27	2	paper	paper	NOUN
ejpam-4830	27	3	is	be	AUX
ejpam-4830	27	4	organized	organize	VERB
ejpam-4830	27	5	as	as	SCONJ
ejpam-4830	27	6	follows	follow	VERB
ejpam-4830	27	7	.	.	PUNCT
ejpam-4830	28	1	in	in	ADP
ejpam-4830	28	2	section	section	NOUN
ejpam-4830	28	3	2	2	NUM
ejpam-4830	28	4	we	we	PRON
ejpam-4830	28	5	present	present	VERB
ejpam-4830	28	6	the	the	DET
ejpam-4830	28	7	definition	definition	NOUN
ejpam-4830	28	8	of	of	ADP
ejpam-4830	28	9	the	the	DET
ejpam-4830	28	10	british	british	ADJ
ejpam-4830	28	11	put	put	NOUN
ejpam-4830	28	12	option	option	NOUN
ejpam-4830	28	13	as	as	SCONJ
ejpam-4830	28	14	given	give	VERB
ejpam-4830	28	15	in	in	ADP
ejpam-4830	28	16	[	[	X
ejpam-4830	28	17	5	5	NUM
ejpam-4830	28	18	]	]	PUNCT
ejpam-4830	28	19	and	and	CCONJ
ejpam-4830	28	20	the	the	DET
ejpam-4830	28	21	financial	financial	ADJ
ejpam-4830	28	22	setting	setting	NOUN
ejpam-4830	28	23	.	.	PUNCT
ejpam-4830	29	1	in	in	ADP
ejpam-4830	29	2	section	section	NOUN
ejpam-4830	29	3	3	3	NUM
ejpam-4830	29	4	we	we	PRON
ejpam-4830	29	5	define	define	VERB
ejpam-4830	29	6	the	the	DET
ejpam-4830	29	7	stopping	stopping	NOUN
ejpam-4830	29	8	set	set	VERB
ejpam-4830	29	9	and	and	CCONJ
ejpam-4830	29	10	boundary	boundary	ADJ
ejpam-4830	29	11	function	function	NOUN
ejpam-4830	29	12	and	and	CCONJ
ejpam-4830	29	13	provide	provide	VERB
ejpam-4830	29	14	results	result	NOUN
ejpam-4830	29	15	involving	involve	VERB
ejpam-4830	29	16	these	these	DET
ejpam-4830	29	17	two	two	NUM
ejpam-4830	29	18	.	.	PUNCT
ejpam-4830	30	1	in	in	ADP
ejpam-4830	30	2	particular	particular	ADJ
ejpam-4830	30	3	,	,	PUNCT
ejpam-4830	30	4	we	we	PRON
ejpam-4830	30	5	show	show	VERB
ejpam-4830	30	6	that	that	SCONJ
ejpam-4830	30	7	the	the	DET
ejpam-4830	30	8	boundary	boundary	ADJ
ejpam-4830	30	9	function	function	NOUN
ejpam-4830	30	10	satisfies	satisfy	VERB
ejpam-4830	30	11	the	the	DET
ejpam-4830	30	12	volterra	volterra	NOUN
ejpam-4830	30	13	type	type	NOUN
ejpam-4830	30	14	equation	equation	NOUN
ejpam-4830	30	15	,	,	PUNCT
ejpam-4830	30	16	then	then	ADV
ejpam-4830	30	17	conclude	conclude	VERB
ejpam-4830	30	18	.	.	PUNCT
ejpam-4830	31	1	2	2	X
ejpam-4830	31	2	.	.	X
ejpam-4830	31	3	setting	setting	NOUN
ejpam-4830	31	4	of	of	ADP
ejpam-4830	31	5	the	the	DET
ejpam-4830	31	6	problem	problem	NOUN
ejpam-4830	31	7	in	in	ADP
ejpam-4830	31	8	this	this	DET
ejpam-4830	31	9	paper	paper	NOUN
ejpam-4830	31	10	,	,	PUNCT
ejpam-4830	31	11	we	we	PRON
ejpam-4830	31	12	assume	assume	VERB
ejpam-4830	31	13	that	that	SCONJ
ejpam-4830	31	14	the	the	DET
ejpam-4830	31	15	economic	economic	ADJ
ejpam-4830	31	16	state	state	NOUN
ejpam-4830	31	17	of	of	ADP
ejpam-4830	31	18	the	the	DET
ejpam-4830	31	19	world	world	NOUN
ejpam-4830	31	20	is	be	AUX
ejpam-4830	31	21	described	describe	VERB
ejpam-4830	31	22	by	by	ADP
ejpam-4830	31	23	a	a	DET
ejpam-4830	31	24	finite	finite	ADJ
ejpam-4830	31	25	state	state	NOUN
ejpam-4830	31	26	continuous	continuous	ADJ
ejpam-4830	31	27	-	-	PUNCT
ejpam-4830	31	28	time	time	NOUN
ejpam-4830	31	29	markov	markov	NOUN
ejpam-4830	31	30	chain	chain	NOUN
ejpam-4830	31	31	α	α	NOUN
ejpam-4830	31	32	=	=	PUNCT
ejpam-4830	31	33	(	(	PUNCT
ejpam-4830	31	34	αt)t∈r+	αt)t∈r+	NOUN
ejpam-4830	31	35	on	on	ADP
ejpam-4830	31	36	m	m	NOUN
ejpam-4830	31	37	=	=	PUNCT
ejpam-4830	31	38	{	{	PUNCT
ejpam-4830	31	39	1	1	NUM
ejpam-4830	31	40	,	,	PUNCT
ejpam-4830	31	41	2	2	NUM
ejpam-4830	31	42	,	,	PUNCT
ejpam-4830	31	43	.	.	PUNCT
ejpam-4830	31	44	.	.	PUNCT
ejpam-4830	31	45	.	.	PUNCT
ejpam-4830	32	1	,	,	PUNCT
ejpam-4830	32	2	m	m	VERB
ejpam-4830	32	3	}	}	PUNCT
ejpam-4830	32	4	.	.	PUNCT
ejpam-4830	33	1	suppose	suppose	VERB
ejpam-4830	33	2	that	that	SCONJ
ejpam-4830	33	3	the	the	DET
ejpam-4830	33	4	volatility	volatility	NOUN
ejpam-4830	33	5	σ	σ	NOUN
ejpam-4830	33	6	:	:	PUNCT
ejpam-4830	33	7	m	m	VERB
ejpam-4830	33	8	→	→	PUNCT
ejpam-4830	33	9	(	(	PUNCT
ejpam-4830	33	10	0,∞	0,∞	NUM
ejpam-4830	33	11	)	)	PUNCT
ejpam-4830	33	12	depends	depend	VERB
ejpam-4830	33	13	on	on	ADP
ejpam-4830	33	14	the	the	DET
ejpam-4830	33	15	state	state	NOUN
ejpam-4830	33	16	α	α	NOUN
ejpam-4830	33	17	of	of	ADP
ejpam-4830	33	18	the	the	DET
ejpam-4830	33	19	economy	economy	NOUN
ejpam-4830	33	20	.	.	PUNCT
ejpam-4830	34	1	under	under	ADP
ejpam-4830	34	2	the	the	DET
ejpam-4830	34	3	real	real	ADJ
ejpam-4830	34	4	world	world	NOUN
ejpam-4830	34	5	probability	probability	NOUN
ejpam-4830	34	6	measure	measure	NOUN
ejpam-4830	34	7	p	p	X
ejpam-4830	34	8	,	,	PUNCT
ejpam-4830	34	9	we	we	PRON
ejpam-4830	34	10	assume	assume	VERB
ejpam-4830	34	11	that	that	SCONJ
ejpam-4830	34	12	the	the	DET
ejpam-4830	34	13	dynamics	dynamic	NOUN
ejpam-4830	34	14	of	of	ADP
ejpam-4830	34	15	the	the	DET
ejpam-4830	34	16	stock	stock	NOUN
ejpam-4830	34	17	price	price	NOUN
ejpam-4830	34	18	process	process	NOUN
ejpam-4830	34	19	follows	follow	VERB
ejpam-4830	34	20	a	a	DET
ejpam-4830	34	21	geometric	geometric	ADJ
ejpam-4830	34	22	brownian	brownian	ADJ
ejpam-4830	34	23	motion	motion	NOUN
ejpam-4830	34	24	:	:	PUNCT
ejpam-4830	35	1	dxt	dxt	PROPN
ejpam-4830	35	2	=	=	PUNCT
ejpam-4830	35	3	µxtdt+	µxtdt+	ADP
ejpam-4830	35	4	σ(αt)xtdwt	σ(αt)xtdwt	NOUN
ejpam-4830	35	5	,	,	PUNCT
ejpam-4830	35	6	x0	x0	PROPN
ejpam-4830	35	7	=	=	PUNCT
ejpam-4830	35	8	x	x	X
ejpam-4830	35	9	>	>	X
ejpam-4830	35	10	0	0	NUM
ejpam-4830	35	11	,	,	PUNCT
ejpam-4830	35	12	(	(	PUNCT
ejpam-4830	35	13	1	1	X
ejpam-4830	35	14	)	)	PUNCT
ejpam-4830	35	15	where	where	SCONJ
ejpam-4830	35	16	µ	µ	X
ejpam-4830	35	17	∈	∈	NOUN
ejpam-4830	35	18	r	r	NOUN
ejpam-4830	35	19	is	be	AUX
ejpam-4830	35	20	the	the	DET
ejpam-4830	35	21	true	true	ADJ
ejpam-4830	35	22	drift	drift	NOUN
ejpam-4830	35	23	,	,	PUNCT
ejpam-4830	35	24	w	w	NOUN
ejpam-4830	35	25	=	=	SYM
ejpam-4830	35	26	(	(	PUNCT
ejpam-4830	35	27	wt)t≥0	wt)t≥0	PROPN
ejpam-4830	35	28	denotes	denote	VERB
ejpam-4830	35	29	the	the	DET
ejpam-4830	35	30	standard	standard	ADJ
ejpam-4830	35	31	brownian	brownian	ADJ
ejpam-4830	35	32	motion	motion	NOUN
ejpam-4830	35	33	defined	define	VERB
ejpam-4830	35	34	on	on	ADP
ejpam-4830	35	35	a	a	DET
ejpam-4830	35	36	probability	probability	NOUN
ejpam-4830	35	37	space	space	NOUN
ejpam-4830	35	38	(	(	PUNCT
ejpam-4830	35	39	ω	ω	PROPN
ejpam-4830	35	40	,	,	PUNCT
ejpam-4830	35	41	f	f	PROPN
ejpam-4830	35	42	,	,	PUNCT
ejpam-4830	35	43	p	p	NOUN
ejpam-4830	35	44	)	)	PUNCT
ejpam-4830	35	45	.	.	PUNCT
ejpam-4830	36	1	here	here	ADV
ejpam-4830	36	2	,	,	PUNCT
ejpam-4830	36	3	we	we	PRON
ejpam-4830	36	4	assume	assume	VERB
ejpam-4830	36	5	that	that	SCONJ
ejpam-4830	36	6	w	w	NOUN
ejpam-4830	36	7	is	be	AUX
ejpam-4830	36	8	independent	independent	ADJ
ejpam-4830	36	9	of	of	ADP
ejpam-4830	36	10	the	the	DET
ejpam-4830	36	11	markov	markov	NOUN
ejpam-4830	36	12	-	-	PUNCT
ejpam-4830	36	13	chain	chain	NOUN
ejpam-4830	36	14	α	α	NOUN
ejpam-4830	36	15	and	and	CCONJ
ejpam-4830	36	16	the	the	DET
ejpam-4830	36	17	filtration	filtration	NOUN
ejpam-4830	36	18	f	f	NOUN
ejpam-4830	37	1	=	=	PUNCT
ejpam-4830	37	2	(	(	PUNCT
ejpam-4830	37	3	ft)t∈r+	ft)t∈r+	NOUN
ejpam-4830	37	4	is	be	AUX
ejpam-4830	37	5	generated	generate	VERB
ejpam-4830	37	6	by	by	ADP
ejpam-4830	37	7	w	w	PROPN
ejpam-4830	37	8	and	and	CCONJ
ejpam-4830	37	9	α	α	NOUN
ejpam-4830	37	10	.	.	PUNCT
ejpam-4830	38	1	we	we	PRON
ejpam-4830	38	2	will	will	AUX
ejpam-4830	38	3	consider	consider	VERB
ejpam-4830	38	4	the	the	DET
ejpam-4830	38	5	british	british	ADJ
ejpam-4830	38	6	put	put	VERB
ejpam-4830	38	7	option	option	NOUN
ejpam-4830	38	8	on	on	ADP
ejpam-4830	38	9	stocks	stock	NOUN
ejpam-4830	38	10	in	in	ADP
ejpam-4830	38	11	the	the	DET
ejpam-4830	38	12	aforementioned	aforementioned	ADJ
ejpam-4830	38	13	financial	financial	ADJ
ejpam-4830	38	14	market	market	NOUN
ejpam-4830	38	15	.	.	PUNCT
ejpam-4830	39	1	the	the	DET
ejpam-4830	39	2	british	british	ADJ
ejpam-4830	39	3	put	put	VERB
ejpam-4830	39	4	option	option	NOUN
ejpam-4830	39	5	with	with	ADP
ejpam-4830	39	6	strike	strike	NOUN
ejpam-4830	39	7	price	price	NOUN
ejpam-4830	39	8	k	k	NOUN
ejpam-4830	39	9	and	and	CCONJ
ejpam-4830	39	10	time	time	NOUN
ejpam-4830	39	11	to	to	ADP
ejpam-4830	39	12	maturity	maturity	NOUN
ejpam-4830	39	13	t	t	NOUN
ejpam-4830	39	14	(	(	PUNCT
ejpam-4830	39	15	in	in	ADP
ejpam-4830	39	16	years	year	NOUN
ejpam-4830	39	17	)	)	PUNCT
ejpam-4830	39	18	is	be	AUX
ejpam-4830	39	19	defined	define	VERB
ejpam-4830	39	20	in	in	ADP
ejpam-4830	39	21	[	[	X
ejpam-4830	39	22	5	5	NUM
ejpam-4830	39	23	]	]	PUNCT
ejpam-4830	39	24	as	as	SCONJ
ejpam-4830	39	25	follows	follow	VERB
ejpam-4830	39	26	:	:	PUNCT
ejpam-4830	39	27	definition	definition	NOUN
ejpam-4830	39	28	1	1	NUM
ejpam-4830	39	29	.	.	PUNCT
ejpam-4830	40	1	[	[	X
ejpam-4830	40	2	5	5	X
ejpam-4830	40	3	]	]	PUNCT
ejpam-4830	40	4	the	the	DET
ejpam-4830	40	5	british	british	ADJ
ejpam-4830	40	6	put	put	NOUN
ejpam-4830	40	7	option	option	NOUN
ejpam-4830	40	8	is	be	AUX
ejpam-4830	40	9	a	a	DET
ejpam-4830	40	10	financial	financial	ADJ
ejpam-4830	40	11	contract	contract	NOUN
ejpam-4830	40	12	between	between	ADP
ejpam-4830	40	13	a	a	DET
ejpam-4830	40	14	seller	seller	NOUN
ejpam-4830	40	15	/	/	SYM
ejpam-4830	40	16	hedger	hedger	NOUN
ejpam-4830	40	17	and	and	CCONJ
ejpam-4830	40	18	a	a	DET
ejpam-4830	40	19	buyer	buyer	NOUN
ejpam-4830	40	20	/	/	SYM
ejpam-4830	40	21	holder	holder	NOUN
ejpam-4830	40	22	entitling	entitle	VERB
ejpam-4830	40	23	the	the	DET
ejpam-4830	40	24	latter	latter	ADJ
ejpam-4830	40	25	to	to	PART
ejpam-4830	40	26	exercise	exercise	VERB
ejpam-4830	40	27	at	at	ADP
ejpam-4830	40	28	any	any	DET
ejpam-4830	40	29	(	(	PUNCT
ejpam-4830	40	30	stopping	stopping	NOUN
ejpam-4830	40	31	)	)	PUNCT
ejpam-4830	40	32	time	time	NOUN
ejpam-4830	40	33	τ	τ	X
ejpam-4830	40	34	prior	prior	ADV
ejpam-4830	40	35	to	to	ADP
ejpam-4830	40	36	maturity	maturity	NOUN
ejpam-4830	40	37	t	t	NOUN
ejpam-4830	40	38	whereupon	whereupon	ADV
ejpam-4830	40	39	his	his	PRON
ejpam-4830	40	40	payoff	payoff	NOUN
ejpam-4830	40	41	(	(	PUNCT
ejpam-4830	40	42	deliverable	deliverable	VERB
ejpam-4830	40	43	immediately	immediately	ADV
ejpam-4830	40	44	)	)	PUNCT
ejpam-4830	40	45	is	be	AUX
ejpam-4830	40	46	the	the	DET
ejpam-4830	40	47	’	'	PUNCT
ejpam-4830	40	48	best	good	ADJ
ejpam-4830	40	49	prediction	prediction	NOUN
ejpam-4830	40	50	’	'	PUNCT
ejpam-4830	40	51	of	of	ADP
ejpam-4830	40	52	the	the	DET
ejpam-4830	40	53	european	european	PROPN
ejpam-4830	40	54	f.	f.	PROPN
ejpam-4830	40	55	sumalpong	sumalpong	PROPN
ejpam-4830	40	56	,	,	PUNCT
ejpam-4830	40	57	m.	m.	PROPN
ejpam-4830	40	58	frondoza	frondoza	PROPN
ejpam-4830	40	59	,	,	PUNCT
ejpam-4830	40	60	n.l	n.l	PROPN
ejpam-4830	40	61	.	.	PROPN
ejpam-4830	40	62	sayson	sayson	PROPN
ejpam-4830	40	63	/	/	SYM
ejpam-4830	40	64	eur	eur	PROPN
ejpam-4830	40	65	.	.	PUNCT
ejpam-4830	41	1	j.	j.	PROPN
ejpam-4830	41	2	pure	pure	PROPN
ejpam-4830	41	3	appl	appl	PROPN
ejpam-4830	41	4	.	.	PROPN
ejpam-4830	41	5	math	math	PROPN
ejpam-4830	41	6	,	,	PUNCT
ejpam-4830	41	7	16	16	NUM
ejpam-4830	41	8	(	(	PUNCT
ejpam-4830	41	9	3	3	NUM
ejpam-4830	41	10	)	)	PUNCT
ejpam-4830	41	11	(	(	PUNCT
ejpam-4830	41	12	2023	2023	NUM
ejpam-4830	41	13	)	)	PUNCT
ejpam-4830	41	14	,	,	PUNCT
ejpam-4830	41	15	1830	1830	NUM
ejpam-4830	41	16	-	-	SYM
ejpam-4830	41	17	1847	1847	NUM
ejpam-4830	41	18	1832	1832	NUM
ejpam-4830	41	19	payoff	payoff	NOUN
ejpam-4830	41	20	(	(	PUNCT
ejpam-4830	41	21	k	k	PROPN
ejpam-4830	41	22	−	−	PROPN
ejpam-4830	41	23	xt	xt	PROPN
ejpam-4830	41	24	)	)	PUNCT
ejpam-4830	42	1	+	+	CCONJ
ejpam-4830	42	2	given	give	VERB
ejpam-4830	42	3	all	all	DET
ejpam-4830	42	4	the	the	DET
ejpam-4830	42	5	information	information	NOUN
ejpam-4830	42	6	up	up	ADP
ejpam-4830	42	7	to	to	ADP
ejpam-4830	42	8	time	time	NOUN
ejpam-4830	42	9	τ	τ	X
ejpam-4830	42	10	under	under	ADP
ejpam-4830	42	11	the	the	DET
ejpam-4830	42	12	hypothesis	hypothesis	NOUN
ejpam-4830	42	13	that	that	PRON
ejpam-4830	42	14	the	the	DET
ejpam-4830	42	15	true	true	ADJ
ejpam-4830	42	16	drift	drift	NOUN
ejpam-4830	42	17	µ	µ	PROPN
ejpam-4830	42	18	of	of	ADP
ejpam-4830	42	19	the	the	DET
ejpam-4830	42	20	stock	stock	NOUN
ejpam-4830	42	21	price	price	NOUN
ejpam-4830	42	22	equals	equal	VERB
ejpam-4830	42	23	the	the	DET
ejpam-4830	42	24	contract	contract	NOUN
ejpam-4830	42	25	drift	drift	NOUN
ejpam-4830	42	26	µc	µc	PROPN
ejpam-4830	42	27	.	.	PUNCT
ejpam-4830	42	28	in	in	ADP
ejpam-4830	42	29	[	[	X
ejpam-4830	42	30	5	5	NUM
ejpam-4830	42	31	]	]	PUNCT
ejpam-4830	42	32	,	,	PUNCT
ejpam-4830	42	33	the	the	DET
ejpam-4830	42	34	price	price	NOUN
ejpam-4830	42	35	of	of	ADP
ejpam-4830	42	36	the	the	DET
ejpam-4830	42	37	british	british	ADJ
ejpam-4830	42	38	put	put	NOUN
ejpam-4830	42	39	option	option	NOUN
ejpam-4830	42	40	is	be	AUX
ejpam-4830	42	41	derived	derive	VERB
ejpam-4830	42	42	under	under	ADP
ejpam-4830	42	43	the	the	DET
ejpam-4830	42	44	hypothesis	hypothesis	NOUN
ejpam-4830	42	45	that	that	PRON
ejpam-4830	42	46	the	the	DET
ejpam-4830	42	47	volatility	volatility	NOUN
ejpam-4830	42	48	is	be	AUX
ejpam-4830	42	49	constant	constant	ADJ
ejpam-4830	42	50	for	for	ADP
ejpam-4830	42	51	all	all	DET
ejpam-4830	42	52	t	t	NOUN
ejpam-4830	42	53	∈	∈	PROPN
ejpam-4830	43	1	[	[	X
ejpam-4830	43	2	0	0	NUM
ejpam-4830	43	3	,	,	PUNCT
ejpam-4830	43	4	t	t	X
ejpam-4830	43	5	]	]	PUNCT
ejpam-4830	43	6	.	.	PUNCT
ejpam-4830	44	1	hence	hence	ADV
ejpam-4830	44	2	,	,	PUNCT
ejpam-4830	44	3	this	this	DET
ejpam-4830	44	4	paper	paper	NOUN
ejpam-4830	44	5	presents	present	VERB
ejpam-4830	44	6	an	an	DET
ejpam-4830	44	7	extension	extension	NOUN
ejpam-4830	44	8	of	of	ADP
ejpam-4830	44	9	the	the	DET
ejpam-4830	44	10	results	result	NOUN
ejpam-4830	44	11	in	in	ADP
ejpam-4830	44	12	[	[	X
ejpam-4830	44	13	5	5	NUM
ejpam-4830	44	14	]	]	PUNCT
ejpam-4830	44	15	.	.	PUNCT
ejpam-4830	45	1	for	for	ADP
ejpam-4830	45	2	0	0	NUM
ejpam-4830	45	3	≤	≤	NUM
ejpam-4830	45	4	t	t	PROPN
ejpam-4830	45	5	≤	≤	PROPN
ejpam-4830	45	6	t	t	NOUN
ejpam-4830	45	7	,	,	PUNCT
ejpam-4830	45	8	let	let	VERB
ejpam-4830	45	9	β(t	β(t	PROPN
ejpam-4830	45	10	)	)	PUNCT
ejpam-4830	46	1	:	:	PUNCT
ejpam-4830	46	2	=	=	PRON
ejpam-4830	46	3	µc	µc	ADP
ejpam-4830	46	4	−	−	PROPN
ejpam-4830	46	5	µ	µ	PRON
ejpam-4830	46	6	σ(αt	σ(αt	NOUN
ejpam-4830	46	7	)	)	PUNCT
ejpam-4830	46	8	,	,	PUNCT
ejpam-4830	46	9	(	(	PUNCT
ejpam-4830	46	10	2	2	X
ejpam-4830	46	11	)	)	PUNCT
ejpam-4830	46	12	where	where	SCONJ
ejpam-4830	46	13	µc	µc	AUX
ejpam-4830	46	14	̸=	̸=	PROPN
ejpam-4830	46	15	µ.	µ.	NOUN
ejpam-4830	46	16	define	define	VERB
ejpam-4830	46	17	an	an	DET
ejpam-4830	46	18	equivalent	equivalent	ADJ
ejpam-4830	46	19	measure	measure	NOUN
ejpam-4830	46	20	pµc	pµc	NOUN
ejpam-4830	46	21	via	via	ADP
ejpam-4830	46	22	the	the	DET
ejpam-4830	46	23	following	following	NOUN
ejpam-4830	46	24	:	:	PUNCT
ejpam-4830	46	25	dpµc	dpµc	ADJ
ejpam-4830	46	26	dp	dp	NOUN
ejpam-4830	46	27	=	=	SYM
ejpam-4830	46	28	zt	zt	PROPN
ejpam-4830	46	29	,	,	PUNCT
ejpam-4830	46	30	(	(	PUNCT
ejpam-4830	46	31	3	3	X
ejpam-4830	46	32	)	)	PUNCT
ejpam-4830	46	33	where	where	SCONJ
ejpam-4830	46	34	zt	zt	PROPN
ejpam-4830	46	35	:	:	PUNCT
ejpam-4830	46	36	=	=	SYM
ejpam-4830	46	37	exp	exp	PROPN
ejpam-4830	46	38	[	[	X
ejpam-4830	46	39	∫	∫	X
ejpam-4830	46	40	t	t	PROPN
ejpam-4830	46	41	0	0	NUM
ejpam-4830	46	42	β(u)dwu	β(u)dwu	NOUN
ejpam-4830	46	43	−	−	NUM
ejpam-4830	46	44	1	1	NUM
ejpam-4830	46	45	2	2	NUM
ejpam-4830	46	46	∫	∫	NOUN
ejpam-4830	46	47	t	t	PROPN
ejpam-4830	46	48	0	0	NUM
ejpam-4830	46	49	β2(u)du	β2(u)du	NUM
ejpam-4830	46	50	]	]	X
ejpam-4830	46	51	(	(	PUNCT
ejpam-4830	46	52	4	4	NUM
ejpam-4830	46	53	)	)	PUNCT
ejpam-4830	46	54	and	and	CCONJ
ejpam-4830	46	55	e[zt	e[zt	X
ejpam-4830	46	56	]	]	X
ejpam-4830	46	57	=	=	SYM
ejpam-4830	46	58	1	1	NUM
ejpam-4830	46	59	for	for	ADP
ejpam-4830	46	60	0	0	NUM
ejpam-4830	46	61	≤	≤	NUM
ejpam-4830	46	62	t	t	PROPN
ejpam-4830	46	63	≤	≤	PROPN
ejpam-4830	46	64	t	t	PROPN
ejpam-4830	46	65	.	.	PUNCT
ejpam-4830	47	1	then	then	ADV
ejpam-4830	47	2	by	by	ADP
ejpam-4830	47	3	itô′s	itô′s	PROPN
ejpam-4830	47	4	formula	formula	NOUN
ejpam-4830	47	5	,	,	PUNCT
ejpam-4830	47	6	dzt	dzt	NOUN
ejpam-4830	47	7	zt	zt	NOUN
ejpam-4830	47	8	=	=	PUNCT
ejpam-4830	47	9	β(t)dwt	β(t)dwt	PROPN
ejpam-4830	47	10	.	.	PUNCT
ejpam-4830	48	1	(	(	PUNCT
ejpam-4830	48	2	5	5	X
ejpam-4830	48	3	)	)	PUNCT
ejpam-4830	48	4	this	this	PRON
ejpam-4830	48	5	shows	show	VERB
ejpam-4830	48	6	that	that	SCONJ
ejpam-4830	48	7	zt	zt	PROPN
ejpam-4830	48	8	is	be	AUX
ejpam-4830	48	9	a	a	DET
ejpam-4830	48	10	local	local	ADJ
ejpam-4830	48	11	martingale	martingale	NOUN
ejpam-4830	48	12	.	.	PUNCT
ejpam-4830	49	1	from	from	ADP
ejpam-4830	49	2	lemma	lemma	PROPN
ejpam-4830	49	3	1	1	NUM
ejpam-4830	49	4	in	in	ADP
ejpam-4830	49	5	[	[	X
ejpam-4830	49	6	2	2	NUM
ejpam-4830	49	7	]	]	PUNCT
ejpam-4830	49	8	,	,	PUNCT
ejpam-4830	49	9	we	we	PRON
ejpam-4830	49	10	have	have	VERB
ejpam-4830	49	11	wµc	wµc	NOUN
ejpam-4830	49	12	t	t	NOUN
ejpam-4830	49	13	=	=	PUNCT
ejpam-4830	50	1	wt	wt	ADP
ejpam-4830	50	2	−	−	NUM
ejpam-4830	50	3	∫	∫	PROPN
ejpam-4830	50	4	t	t	PROPN
ejpam-4830	50	5	0	0	NUM
ejpam-4830	50	6	β(u)du	β(u)du	PUNCT
ejpam-4830	50	7	(	(	PUNCT
ejpam-4830	50	8	6	6	NUM
ejpam-4830	50	9	)	)	PUNCT
ejpam-4830	50	10	is	be	AUX
ejpam-4830	50	11	a	a	DET
ejpam-4830	50	12	pµc	pµc	ADJ
ejpam-4830	50	13	-	-	PUNCT
ejpam-4830	50	14	brownian	brownian	ADJ
ejpam-4830	50	15	motion	motion	NOUN
ejpam-4830	50	16	.	.	PUNCT
ejpam-4830	51	1	under	under	ADP
ejpam-4830	51	2	the	the	DET
ejpam-4830	51	3	probability	probability	NOUN
ejpam-4830	51	4	measure	measure	NOUN
ejpam-4830	51	5	pµc	pµc	PROPN
ejpam-4830	51	6	,	,	PUNCT
ejpam-4830	51	7	(	(	PUNCT
ejpam-4830	51	8	1	1	X
ejpam-4830	51	9	)	)	PUNCT
ejpam-4830	51	10	becomes	become	VERB
ejpam-4830	51	11	dxt	dxt	PROPN
ejpam-4830	51	12	=	=	PUNCT
ejpam-4830	52	1	µcxtdt+	µcxtdt+	PUNCT
ejpam-4830	52	2	σ(αt)xtdw	σ(αt)xtdw	PROPN
ejpam-4830	52	3	µc	µc	PROPN
ejpam-4830	52	4	t	t	NOUN
ejpam-4830	52	5	(	(	PUNCT
ejpam-4830	52	6	7	7	NUM
ejpam-4830	52	7	)	)	PUNCT
ejpam-4830	53	1	where	where	SCONJ
ejpam-4830	53	2	0	0	NUM
ejpam-4830	53	3	≤	≤	NUM
ejpam-4830	53	4	t	t	PROPN
ejpam-4830	53	5	≤	≤	X
ejpam-4830	53	6	t	t	PROPN
ejpam-4830	53	7	with	with	ADP
ejpam-4830	53	8	x0	x0	PROPN
ejpam-4830	53	9	=	=	PUNCT
ejpam-4830	53	10	x	x	SYM
ejpam-4830	53	11	∈	∈	PROPN
ejpam-4830	53	12	(	(	PUNCT
ejpam-4830	53	13	0,∞	0,∞	NOUN
ejpam-4830	53	14	)	)	PUNCT
ejpam-4830	53	15	.	.	PUNCT
ejpam-4830	54	1	thus	thus	ADV
ejpam-4830	54	2	,	,	PUNCT
ejpam-4830	54	3	making	make	VERB
ejpam-4830	54	4	use	use	NOUN
ejpam-4830	54	5	of	of	ADP
ejpam-4830	54	6	(	(	PUNCT
ejpam-4830	54	7	3	3	NUM
ejpam-4830	54	8	)	)	PUNCT
ejpam-4830	54	9	,	,	PUNCT
ejpam-4830	54	10	we	we	PRON
ejpam-4830	54	11	have	have	VERB
ejpam-4830	54	12	eµc(x	eµc(x	NOUN
ejpam-4830	54	13	)	)	PUNCT
ejpam-4830	54	14	=	=	SYM
ejpam-4830	54	15	e(ztx	e(ztx	PROPN
ejpam-4830	54	16	)	)	PUNCT
ejpam-4830	54	17	=	=	SYM
ejpam-4830	54	18	e(zt	e(zt	PROPN
ejpam-4830	54	19	)	)	PUNCT
ejpam-4830	54	20	e(x	e(x	NUM
ejpam-4830	54	21	)	)	PUNCT
ejpam-4830	54	22	=	=	SYM
ejpam-4830	54	23	e(x	e(x	NUM
ejpam-4830	54	24	)	)	PUNCT
ejpam-4830	54	25	for	for	ADP
ejpam-4830	54	26	any	any	DET
ejpam-4830	54	27	random	random	ADJ
ejpam-4830	54	28	variable	variable	NOUN
ejpam-4830	54	29	x.	x.	NOUN
ejpam-4830	55	1	the	the	DET
ejpam-4830	55	2	payoff	payoff	NOUN
ejpam-4830	55	3	of	of	ADP
ejpam-4830	55	4	the	the	DET
ejpam-4830	55	5	british	british	ADJ
ejpam-4830	55	6	put	put	NOUN
ejpam-4830	55	7	option	option	NOUN
ejpam-4830	55	8	at	at	ADP
ejpam-4830	55	9	a	a	DET
ejpam-4830	55	10	given	give	VERB
ejpam-4830	55	11	stopping	stopping	NOUN
ejpam-4830	55	12	time	time	NOUN
ejpam-4830	55	13	t	t	PROPN
ejpam-4830	55	14	=	=	PUNCT
ejpam-4830	55	15	τ	τ	PROPN
ejpam-4830	55	16	is	be	AUX
ejpam-4830	55	17	given	give	VERB
ejpam-4830	55	18	by	by	ADP
ejpam-4830	55	19	eµc	eµc	PROPN
ejpam-4830	55	20	[	[	PUNCT
ejpam-4830	55	21	(	(	PUNCT
ejpam-4830	55	22	k	k	NOUN
ejpam-4830	55	23	−xt	−xt	PROPN
ejpam-4830	55	24	)	)	PUNCT
ejpam-4830	56	1	+	+	CCONJ
ejpam-4830	56	2	|	|	ADV
ejpam-4830	56	3	fτ	fτ	X
ejpam-4830	56	4	]	]	X
ejpam-4830	56	5	(	(	PUNCT
ejpam-4830	56	6	8)	8)	NUM
ejpam-4830	56	7	where	where	SCONJ
ejpam-4830	56	8	the	the	DET
ejpam-4830	56	9	conditional	conditional	ADJ
ejpam-4830	56	10	expectation	expectation	NOUN
ejpam-4830	56	11	is	be	AUX
ejpam-4830	56	12	taken	take	VERB
ejpam-4830	56	13	with	with	ADP
ejpam-4830	56	14	respect	respect	NOUN
ejpam-4830	56	15	to	to	ADP
ejpam-4830	56	16	a	a	DET
ejpam-4830	56	17	new	new	ADJ
ejpam-4830	56	18	(	(	PUNCT
ejpam-4830	56	19	equivalent	equivalent	ADJ
ejpam-4830	56	20	)	)	PUNCT
ejpam-4830	56	21	probability	probability	NOUN
ejpam-4830	56	22	measure	measure	NOUN
ejpam-4830	56	23	pµc	pµc	NOUN
ejpam-4830	56	24	under	under	ADP
ejpam-4830	56	25	which	which	PRON
ejpam-4830	56	26	the	the	DET
ejpam-4830	56	27	stock	stock	NOUN
ejpam-4830	56	28	price	price	NOUN
ejpam-4830	56	29	x	x	VERB
ejpam-4830	56	30	evolves	evolve	VERB
ejpam-4830	56	31	as	as	ADP
ejpam-4830	56	32	in	in	ADP
ejpam-4830	56	33	(	(	PUNCT
ejpam-4830	56	34	7	7	NUM
ejpam-4830	56	35	)	)	PUNCT
ejpam-4830	56	36	with	with	ADP
ejpam-4830	56	37	x0	x0	PROPN
ejpam-4830	56	38	=	=	PUNCT
ejpam-4830	56	39	x	x	SYM
ejpam-4830	56	40	∈	∈	PROPN
ejpam-4830	56	41	(	(	PUNCT
ejpam-4830	56	42	0,∞	0,∞	NOUN
ejpam-4830	56	43	)	)	PUNCT
ejpam-4830	56	44	.	.	PUNCT
ejpam-4830	57	1	thus	thus	ADV
ejpam-4830	57	2	,	,	PUNCT
ejpam-4830	57	3	the	the	DET
ejpam-4830	57	4	effect	effect	NOUN
ejpam-4830	57	5	of	of	ADP
ejpam-4830	57	6	exercising	exercise	VERB
ejpam-4830	57	7	the	the	DET
ejpam-4830	57	8	british	british	ADJ
ejpam-4830	57	9	put	put	NOUN
ejpam-4830	57	10	option	option	NOUN
ejpam-4830	57	11	is	be	AUX
ejpam-4830	57	12	to	to	PART
ejpam-4830	57	13	substitute	substitute	VERB
ejpam-4830	57	14	the	the	DET
ejpam-4830	57	15	contract	contract	NOUN
ejpam-4830	57	16	drift	drift	NOUN
ejpam-4830	57	17	µc	µc	ADP
ejpam-4830	57	18	to	to	ADP
ejpam-4830	57	19	the	the	DET
ejpam-4830	57	20	true	true	ADJ
ejpam-4830	57	21	(	(	PUNCT
ejpam-4830	57	22	unknown	unknown	ADJ
ejpam-4830	57	23	)	)	PUNCT
ejpam-4830	57	24	drift	drift	NOUN
ejpam-4830	57	25	µ	µ	PROPN
ejpam-4830	57	26	of	of	ADP
ejpam-4830	57	27	the	the	DET
ejpam-4830	57	28	stock	stock	NOUN
ejpam-4830	57	29	price	price	NOUN
ejpam-4830	57	30	for	for	ADP
ejpam-4830	57	31	the	the	DET
ejpam-4830	57	32	remaining	remain	VERB
ejpam-4830	57	33	time	time	NOUN
ejpam-4830	57	34	of	of	ADP
ejpam-4830	57	35	the	the	DET
ejpam-4830	57	36	contract	contract	NOUN
ejpam-4830	57	37	.	.	PUNCT
ejpam-4830	58	1	note	note	VERB
ejpam-4830	58	2	that	that	SCONJ
ejpam-4830	58	3	the	the	DET
ejpam-4830	58	4	value	value	NOUN
ejpam-4830	58	5	of	of	ADP
ejpam-4830	58	6	the	the	DET
ejpam-4830	58	7	contract	contract	NOUN
ejpam-4830	58	8	drift	drift	NOUN
ejpam-4830	58	9	µc	µc	VERB
ejpam-4830	58	10	must	must	AUX
ejpam-4830	58	11	be	be	AUX
ejpam-4830	58	12	equivalent	equivalent	ADJ
ejpam-4830	58	13	to	to	ADP
ejpam-4830	58	14	the	the	DET
ejpam-4830	58	15	buyer	buyer	NOUN
ejpam-4830	58	16	’s	’s	PART
ejpam-4830	58	17	tolerance	tolerance	NOUN
ejpam-4830	58	18	level	level	NOUN
ejpam-4830	58	19	for	for	ADP
ejpam-4830	58	20	the	the	DET
ejpam-4830	58	21	deviation	deviation	NOUN
ejpam-4830	58	22	of	of	ADP
ejpam-4830	58	23	the	the	DET
ejpam-4830	58	24	true	true	ADJ
ejpam-4830	58	25	drift	drift	NOUN
ejpam-4830	58	26	µ	µ	NOUN
ejpam-4830	58	27	from	from	ADP
ejpam-4830	58	28	his	his	PRON
ejpam-4830	58	29	original	original	ADJ
ejpam-4830	58	30	belief	belief	NOUN
ejpam-4830	58	31	.	.	PUNCT
ejpam-4830	59	1	moreover	moreover	ADV
ejpam-4830	59	2	,	,	PUNCT
ejpam-4830	59	3	to	to	PART
ejpam-4830	59	4	avoid	avoid	VERB
ejpam-4830	59	5	arbitrage	arbitrage	PROPN
ejpam-4830	59	6	f.	f.	PROPN
ejpam-4830	59	7	sumalpong	sumalpong	PROPN
ejpam-4830	59	8	,	,	PUNCT
ejpam-4830	59	9	m.	m.	PROPN
ejpam-4830	59	10	frondoza	frondoza	PROPN
ejpam-4830	59	11	,	,	PUNCT
ejpam-4830	59	12	n.l	n.l	PROPN
ejpam-4830	59	13	.	.	PROPN
ejpam-4830	59	14	sayson	sayson	PROPN
ejpam-4830	59	15	/	/	SYM
ejpam-4830	59	16	eur	eur	PROPN
ejpam-4830	59	17	.	.	PUNCT
ejpam-4830	60	1	j.	j.	PROPN
ejpam-4830	60	2	pure	pure	PROPN
ejpam-4830	60	3	appl	appl	PROPN
ejpam-4830	60	4	.	.	PROPN
ejpam-4830	60	5	math	math	PROPN
ejpam-4830	60	6	,	,	PUNCT
ejpam-4830	60	7	16	16	NUM
ejpam-4830	60	8	(	(	PUNCT
ejpam-4830	60	9	3	3	NUM
ejpam-4830	60	10	)	)	PUNCT
ejpam-4830	60	11	(	(	PUNCT
ejpam-4830	60	12	2023	2023	NUM
ejpam-4830	60	13	)	)	PUNCT
ejpam-4830	60	14	,	,	PUNCT
ejpam-4830	60	15	1830	1830	NUM
ejpam-4830	60	16	-	-	SYM
ejpam-4830	60	17	1847	1847	NUM
ejpam-4830	60	18	1833	1833	NUM
ejpam-4830	60	19	opportunity	opportunity	NOUN
ejpam-4830	60	20	,	,	PUNCT
ejpam-4830	60	21	the	the	DET
ejpam-4830	60	22	contract	contract	NOUN
ejpam-4830	60	23	drift	drift	NOUN
ejpam-4830	60	24	naturally	naturally	ADV
ejpam-4830	60	25	satisfies	satisfy	VERB
ejpam-4830	60	26	(	(	PUNCT
ejpam-4830	60	27	see	see	VERB
ejpam-4830	60	28	[	[	X
ejpam-4830	60	29	5	5	NUM
ejpam-4830	60	30	]	]	SYM
ejpam-4830	60	31	)	)	PUNCT
ejpam-4830	60	32	µc	µc	ADP
ejpam-4830	60	33	>	>	X
ejpam-4830	60	34	r.	r.	PROPN
ejpam-4830	60	35	(	(	PUNCT
ejpam-4830	60	36	9	9	X
ejpam-4830	60	37	)	)	PUNCT
ejpam-4830	60	38	note	note	NOUN
ejpam-4830	60	39	that	that	SCONJ
ejpam-4830	60	40	by	by	ADP
ejpam-4830	60	41	itô	itô	PROPN
ejpam-4830	60	42	’s	’s	PART
ejpam-4830	60	43	formula	formula	NOUN
ejpam-4830	60	44	,	,	PUNCT
ejpam-4830	60	45	the	the	DET
ejpam-4830	60	46	solution	solution	NOUN
ejpam-4830	60	47	to	to	ADP
ejpam-4830	60	48	equation	equation	NOUN
ejpam-4830	60	49	(	(	PUNCT
ejpam-4830	60	50	7	7	X
ejpam-4830	60	51	)	)	PUNCT
ejpam-4830	60	52	is	be	AUX
ejpam-4830	60	53	xt	xt	NOUN
ejpam-4830	60	54	=	=	SYM
ejpam-4830	60	55	xsz	xsz	PROPN
ejpam-4830	60	56	µc	µc	ADP
ejpam-4830	60	57	s	s	PROPN
ejpam-4830	60	58	,	,	PUNCT
ejpam-4830	60	59	t	t	PROPN
ejpam-4830	60	60	(	(	PUNCT
ejpam-4830	60	61	10	10	NUM
ejpam-4830	60	62	)	)	PUNCT
ejpam-4830	60	63	for	for	ADP
ejpam-4830	60	64	0	0	NUM
ejpam-4830	60	65	≤	≤	NUM
ejpam-4830	60	66	s	s	PART
ejpam-4830	60	67	≤	≤	NUM
ejpam-4830	60	68	t	t	NOUN
ejpam-4830	60	69	≤	≤	NOUN
ejpam-4830	60	70	t	t	PROPN
ejpam-4830	60	71	where	where	SCONJ
ejpam-4830	60	72	zµc	zµc	PROPN
ejpam-4830	60	73	s	s	PROPN
ejpam-4830	60	74	,	,	PUNCT
ejpam-4830	60	75	t	t	NOUN
ejpam-4830	60	76	=	=	SYM
ejpam-4830	60	77	exp	exp	NOUN
ejpam-4830	60	78	[	[	X
ejpam-4830	60	79	∫	∫	X
ejpam-4830	60	80	t	t	PROPN
ejpam-4830	60	81	s	s	PROPN
ejpam-4830	60	82	(	(	PUNCT
ejpam-4830	60	83	µc	µc	INTJ
ejpam-4830	60	84	−	−	PROPN
ejpam-4830	60	85	σ2(αu	σ2(αu	PROPN
ejpam-4830	60	86	)	)	PUNCT
ejpam-4830	60	87	2	2	NUM
ejpam-4830	60	88	)	)	PUNCT
ejpam-4830	61	1	du+	du+	NOUN
ejpam-4830	62	1	∫	∫	PROPN
ejpam-4830	63	1	t	t	PROPN
ejpam-4830	63	2	s	s	PROPN
ejpam-4830	63	3	σ(αu)dw	σ(αu)dw	PROPN
ejpam-4830	63	4	µc	µc	PROPN
ejpam-4830	63	5	u	u	PROPN
ejpam-4830	63	6	]	]	X
ejpam-4830	63	7	(	(	PUNCT
ejpam-4830	63	8	11	11	NUM
ejpam-4830	63	9	)	)	PUNCT
ejpam-4830	63	10	so	so	SCONJ
ejpam-4830	63	11	that	that	SCONJ
ejpam-4830	63	12	the	the	DET
ejpam-4830	63	13	payoff	payoff	NOUN
ejpam-4830	63	14	(	(	PUNCT
ejpam-4830	63	15	8)	8)	NUM
ejpam-4830	63	16	can	can	AUX
ejpam-4830	63	17	be	be	AUX
ejpam-4830	63	18	written	write	VERB
ejpam-4830	63	19	as	as	ADP
ejpam-4830	63	20	eµc	eµc	PROPN
ejpam-4830	63	21	[	[	PUNCT
ejpam-4830	63	22	(	(	PUNCT
ejpam-4830	63	23	k	k	X
ejpam-4830	63	24	−xτz	−xτz	NOUN
ejpam-4830	63	25	µc	µc	PROPN
ejpam-4830	63	26	τ	τ	PROPN
ejpam-4830	63	27	,	,	PUNCT
ejpam-4830	63	28	t	t	PROPN
ejpam-4830	63	29	)	)	PUNCT
ejpam-4830	64	1	+	+	CCONJ
ejpam-4830	64	2	|	|	ADV
ejpam-4830	64	3	fτ	fτ	ADP
ejpam-4830	64	4	]	]	PUNCT
ejpam-4830	64	5	.	.	PUNCT
ejpam-4830	65	1	(	(	PUNCT
ejpam-4830	65	2	12	12	NUM
ejpam-4830	65	3	)	)	PUNCT
ejpam-4830	65	4	let	let	VERB
ejpam-4830	65	5	α0	α0	PROPN
ejpam-4830	65	6	be	be	AUX
ejpam-4830	65	7	given	give	VERB
ejpam-4830	65	8	.	.	PUNCT
ejpam-4830	66	1	applying	apply	VERB
ejpam-4830	66	2	the	the	DET
ejpam-4830	66	3	usual	usual	ADJ
ejpam-4830	66	4	hedging	hedging	NOUN
ejpam-4830	66	5	scheme	scheme	NOUN
ejpam-4830	66	6	,	,	PUNCT
ejpam-4830	66	7	then	then	ADV
ejpam-4830	66	8	the	the	DET
ejpam-4830	66	9	arbitrage	arbitrage	NOUN
ejpam-4830	66	10	-	-	PUNCT
ejpam-4830	66	11	free	free	ADJ
ejpam-4830	66	12	price	price	NOUN
ejpam-4830	66	13	of	of	ADP
ejpam-4830	66	14	the	the	DET
ejpam-4830	66	15	british	british	ADJ
ejpam-4830	66	16	put	put	NOUN
ejpam-4830	66	17	option	option	NOUN
ejpam-4830	66	18	at	at	ADP
ejpam-4830	66	19	deal	deal	NOUN
ejpam-4830	66	20	date	date	NOUN
ejpam-4830	66	21	(	(	PUNCT
ejpam-4830	66	22	time	time	NOUN
ejpam-4830	66	23	0	0	NUM
ejpam-4830	66	24	)	)	PUNCT
ejpam-4830	66	25	is	be	AUX
ejpam-4830	66	26	given	give	VERB
ejpam-4830	66	27	by	by	ADP
ejpam-4830	66	28	v	v	NOUN
ejpam-4830	66	29	=	=	SYM
ejpam-4830	66	30	v	v	NOUN
ejpam-4830	66	31	(	(	PUNCT
ejpam-4830	66	32	0	0	NUM
ejpam-4830	66	33	,	,	PUNCT
ejpam-4830	66	34	x0	x0	PROPN
ejpam-4830	66	35	,	,	PUNCT
ejpam-4830	66	36	α0	α0	ADJ
ejpam-4830	66	37	)	)	PUNCT
ejpam-4830	66	38	=	=	SYM
ejpam-4830	66	39	sup	sup	NOUN
ejpam-4830	66	40	0≤τ≤t	0≤τ≤t	NUM
ejpam-4830	66	41	ẽ	ẽ	PROPN
ejpam-4830	66	42	[	[	PUNCT
ejpam-4830	66	43	e−rτeµc	e−rτeµc	PROPN
ejpam-4830	66	44	(	(	PUNCT
ejpam-4830	66	45	(	(	PUNCT
ejpam-4830	66	46	k	k	NOUN
ejpam-4830	66	47	−xt	−xt	PROPN
ejpam-4830	66	48	)	)	PUNCT
ejpam-4830	67	1	+	+	CCONJ
ejpam-4830	67	2	∣∣fτ	∣∣fτ	ADJ
ejpam-4830	67	3	)	)	PUNCT
ejpam-4830	67	4	∣∣∣f0	∣∣∣f0	PROPN
ejpam-4830	67	5	]	]	PUNCT
ejpam-4830	67	6	(	(	PUNCT
ejpam-4830	67	7	13	13	NUM
ejpam-4830	67	8	)	)	PUNCT
ejpam-4830	67	9	=	=	SYM
ejpam-4830	67	10	sup	sup	NOUN
ejpam-4830	67	11	0≤τ≤t	0≤τ≤t	NUM
ejpam-4830	68	1	ẽ	ẽ	PROPN
ejpam-4830	68	2	[	[	PUNCT
ejpam-4830	68	3	e−rτeµc	e−rτeµc	PROPN
ejpam-4830	68	4	(	(	PUNCT
ejpam-4830	68	5	(	(	PUNCT
ejpam-4830	68	6	k	k	NOUN
ejpam-4830	68	7	−xt	−xt	PROPN
ejpam-4830	68	8	)	)	PUNCT
ejpam-4830	69	1	+	+	CCONJ
ejpam-4830	69	2	∣∣fτ	∣∣fτ	ADJ
ejpam-4830	69	3	)	)	PUNCT
ejpam-4830	69	4	]	]	PUNCT
ejpam-4830	69	5	where	where	SCONJ
ejpam-4830	69	6	the	the	DET
ejpam-4830	69	7	supremum	supremum	NOUN
ejpam-4830	69	8	is	be	AUX
ejpam-4830	69	9	taken	take	VERB
ejpam-4830	69	10	over	over	ADP
ejpam-4830	69	11	all	all	DET
ejpam-4830	69	12	stopping	stop	VERB
ejpam-4830	69	13	time	time	NOUN
ejpam-4830	69	14	τ	τ	X
ejpam-4830	69	15	∈	∈	PROPN
ejpam-4830	69	16	[	[	X
ejpam-4830	69	17	0	0	NUM
ejpam-4830	69	18	,	,	PUNCT
ejpam-4830	69	19	t	t	NOUN
ejpam-4830	69	20	]	]	PUNCT
ejpam-4830	69	21	of	of	ADP
ejpam-4830	69	22	x	x	X
ejpam-4830	69	23	and	and	CCONJ
ejpam-4830	69	24	the	the	DET
ejpam-4830	69	25	ẽ	ẽ	PROPN
ejpam-4830	69	26	is	be	AUX
ejpam-4830	69	27	taken	take	VERB
ejpam-4830	69	28	with	with	ADP
ejpam-4830	69	29	respect	respect	NOUN
ejpam-4830	69	30	to	to	ADP
ejpam-4830	69	31	the	the	DET
ejpam-4830	69	32	(	(	PUNCT
ejpam-4830	69	33	unique	unique	ADJ
ejpam-4830	69	34	)	)	PUNCT
ejpam-4830	69	35	equivalent	equivalent	ADJ
ejpam-4830	69	36	martingale	martingale	NOUN
ejpam-4830	69	37	measure	measure	NOUN
ejpam-4830	69	38	p̃.	p̃.	PROPN
ejpam-4830	69	39	now	now	ADV
ejpam-4830	69	40	,	,	PUNCT
ejpam-4830	69	41	fix	fix	VERB
ejpam-4830	69	42	t	t	X
ejpam-4830	69	43	∈	∈	PROPN
ejpam-4830	70	1	[	[	X
ejpam-4830	70	2	0	0	NUM
ejpam-4830	70	3	,	,	PUNCT
ejpam-4830	70	4	t	t	X
ejpam-4830	70	5	]	]	PUNCT
ejpam-4830	70	6	.	.	PUNCT
ejpam-4830	71	1	we	we	PRON
ejpam-4830	71	2	want	want	VERB
ejpam-4830	71	3	a	a	DET
ejpam-4830	71	4	general	general	ADJ
ejpam-4830	71	5	expression	expression	NOUN
ejpam-4830	71	6	for	for	ADP
ejpam-4830	71	7	the	the	DET
ejpam-4830	71	8	price	price	NOUN
ejpam-4830	71	9	,	,	PUNCT
ejpam-4830	71	10	denoted	denote	VERB
ejpam-4830	71	11	by	by	ADP
ejpam-4830	71	12	v	v	PROPN
ejpam-4830	71	13	(	(	PUNCT
ejpam-4830	71	14	t	t	PROPN
ejpam-4830	71	15	,	,	PUNCT
ejpam-4830	71	16	xt	xt	PROPN
ejpam-4830	71	17	,	,	PUNCT
ejpam-4830	71	18	αt	αt	NOUN
ejpam-4830	71	19	)	)	PUNCT
ejpam-4830	71	20	,	,	PUNCT
ejpam-4830	71	21	of	of	ADP
ejpam-4830	71	22	the	the	DET
ejpam-4830	71	23	british	british	ADJ
ejpam-4830	71	24	put	put	NOUN
ejpam-4830	71	25	option	option	NOUN
ejpam-4830	71	26	at	at	ADP
ejpam-4830	71	27	any	any	DET
ejpam-4830	71	28	time	time	NOUN
ejpam-4830	71	29	t	t	NOUN
ejpam-4830	71	30	at	at	ADP
ejpam-4830	71	31	which	which	PRON
ejpam-4830	71	32	the	the	DET
ejpam-4830	71	33	stock	stock	NOUN
ejpam-4830	71	34	price	price	NOUN
ejpam-4830	71	35	xt	xt	PUNCT
ejpam-4830	72	1	=	=	PUNCT
ejpam-4830	72	2	x	x	X
ejpam-4830	72	3	>	>	X
ejpam-4830	72	4	0	0	X
ejpam-4830	72	5	.	.	PUNCT
ejpam-4830	72	6	denote	denote	VERB
ejpam-4830	72	7	the	the	DET
ejpam-4830	72	8	payoff	payoff	NOUN
ejpam-4830	72	9	in	in	ADP
ejpam-4830	72	10	(	(	PUNCT
ejpam-4830	72	11	8)	8)	NUM
ejpam-4830	72	12	at	at	ADP
ejpam-4830	72	13	τ	τ	X
ejpam-4830	72	14	=	=	SYM
ejpam-4830	72	15	s	s	AUX
ejpam-4830	72	16	by	by	ADP
ejpam-4830	72	17	gµc(s	gµc(	NOUN
ejpam-4830	72	18	,	,	PUNCT
ejpam-4830	72	19	y	y	PROPN
ejpam-4830	72	20	,	,	PUNCT
ejpam-4830	72	21	j	j	NOUN
ejpam-4830	72	22	)	)	PUNCT
ejpam-4830	73	1	=	=	SYM
ejpam-4830	73	2	eµc	eµc	PROPN
ejpam-4830	73	3	[	[	PUNCT
ejpam-4830	73	4	(	(	PUNCT
ejpam-4830	73	5	k	k	NOUN
ejpam-4830	73	6	−	−	PROPN
ejpam-4830	73	7	yzµc	yzµc	PROPN
ejpam-4830	73	8	s	s	PROPN
ejpam-4830	73	9	,	,	PUNCT
ejpam-4830	73	10	t	t	PROPN
ejpam-4830	73	11	)	)	PUNCT
ejpam-4830	74	1	+	+	CCONJ
ejpam-4830	75	1	|	|	ADV
ejpam-4830	75	2	αs	αs	INTJ
ejpam-4830	75	3	=	=	SYM
ejpam-4830	75	4	j	j	PROPN
ejpam-4830	75	5	,	,	PUNCT
ejpam-4830	75	6	xs	xs	PROPN
ejpam-4830	75	7	=	=	SYM
ejpam-4830	75	8	y	y	PROPN
ejpam-4830	75	9	]	]	PUNCT
ejpam-4830	75	10	(	(	PUNCT
ejpam-4830	75	11	14	14	NUM
ejpam-4830	75	12	)	)	PUNCT
ejpam-4830	75	13	for	for	ADP
ejpam-4830	75	14	s	s	PROPN
ejpam-4830	75	15	∈	∈	PROPN
ejpam-4830	76	1	[	[	X
ejpam-4830	76	2	0	0	NUM
ejpam-4830	76	3	,	,	PUNCT
ejpam-4830	76	4	t	t	NOUN
ejpam-4830	76	5	]	]	PUNCT
ejpam-4830	76	6	where	where	SCONJ
ejpam-4830	76	7	zµc	zµc	PROPN
ejpam-4830	76	8	s	s	PROPN
ejpam-4830	76	9	,	,	PUNCT
ejpam-4830	76	10	t	t	PROPN
ejpam-4830	76	11	is	be	AUX
ejpam-4830	76	12	given	give	VERB
ejpam-4830	76	13	in	in	ADP
ejpam-4830	76	14	(	(	PUNCT
ejpam-4830	76	15	11	11	NUM
ejpam-4830	76	16	)	)	PUNCT
ejpam-4830	76	17	.	.	PUNCT
ejpam-4830	77	1	if	if	SCONJ
ejpam-4830	77	2	the	the	DET
ejpam-4830	77	3	exercise	exercise	NOUN
ejpam-4830	77	4	date	date	NOUN
ejpam-4830	77	5	of	of	ADP
ejpam-4830	77	6	the	the	DET
ejpam-4830	77	7	british	british	ADJ
ejpam-4830	77	8	put	put	NOUN
ejpam-4830	77	9	option	option	NOUN
ejpam-4830	77	10	is	be	AUX
ejpam-4830	77	11	at	at	ADP
ejpam-4830	77	12	time	time	NOUN
ejpam-4830	77	13	t+	t+	PUNCT
ejpam-4830	77	14	τ	τ	PROPN
ejpam-4830	77	15	,	,	PUNCT
ejpam-4830	77	16	where	where	SCONJ
ejpam-4830	77	17	τ	τ	PROPN
ejpam-4830	77	18	∈	∈	PROPN
ejpam-4830	78	1	[	[	X
ejpam-4830	78	2	0	0	NUM
ejpam-4830	78	3	,	,	PUNCT
ejpam-4830	78	4	t	t	PROPN
ejpam-4830	78	5	−	−	PROPN
ejpam-4830	78	6	t	t	PROPN
ejpam-4830	78	7	]	]	PUNCT
ejpam-4830	78	8	,	,	PUNCT
ejpam-4830	78	9	then	then	ADV
ejpam-4830	78	10	extending	extend	VERB
ejpam-4830	78	11	the	the	DET
ejpam-4830	78	12	argument	argument	NOUN
ejpam-4830	78	13	in	in	ADP
ejpam-4830	78	14	(	(	PUNCT
ejpam-4830	78	15	13	13	NUM
ejpam-4830	78	16	)	)	PUNCT
ejpam-4830	78	17	,	,	PUNCT
ejpam-4830	78	18	we	we	PRON
ejpam-4830	78	19	have	have	VERB
ejpam-4830	78	20	v	v	NUM
ejpam-4830	78	21	(	(	PUNCT
ejpam-4830	78	22	t	t	PROPN
ejpam-4830	78	23	,	,	PUNCT
ejpam-4830	78	24	x	x	X
ejpam-4830	78	25	,	,	PUNCT
ejpam-4830	78	26	i	i	NOUN
ejpam-4830	78	27	)	)	PUNCT
ejpam-4830	78	28	=	=	PUNCT
ejpam-4830	78	29	sup	sup	NOUN
ejpam-4830	78	30	0≤τ≤t−t	0≤τ≤t−t	NUM
ejpam-4830	78	31	ẽt	ẽt	NOUN
ejpam-4830	78	32	,	,	PUNCT
ejpam-4830	78	33	x	x	X
ejpam-4830	78	34	[	[	PUNCT
ejpam-4830	78	35	e−rτgµc(t+	e−rτgµc(t+	PROPN
ejpam-4830	78	36	τ	τ	PROPN
ejpam-4830	78	37	,	,	PUNCT
ejpam-4830	78	38	xt+τ	xt+τ	PROPN
ejpam-4830	78	39	,	,	PUNCT
ejpam-4830	78	40	j	j	PROPN
ejpam-4830	78	41	)	)	PUNCT
ejpam-4830	79	1	|	|	ADV
ejpam-4830	79	2	αt	αt	NOUN
ejpam-4830	79	3	=	=	SYM
ejpam-4830	79	4	i	i	PROPN
ejpam-4830	79	5	,	,	PUNCT
ejpam-4830	79	6	xt	xt	X
ejpam-4830	80	1	=	=	SYM
ejpam-4830	80	2	x	x	SYM
ejpam-4830	80	3	]	]	X
ejpam-4830	80	4	(	(	PUNCT
ejpam-4830	80	5	15	15	NUM
ejpam-4830	80	6	)	)	PUNCT
ejpam-4830	80	7	where	where	SCONJ
ejpam-4830	80	8	the	the	DET
ejpam-4830	80	9	supremum	supremum	NOUN
ejpam-4830	80	10	is	be	AUX
ejpam-4830	80	11	taken	take	VERB
ejpam-4830	80	12	overall	overall	ADJ
ejpam-4830	80	13	stopping	stopping	NOUN
ejpam-4830	80	14	time	time	NOUN
ejpam-4830	80	15	τ	τ	X
ejpam-4830	80	16	∈	∈	PROPN
ejpam-4830	81	1	[	[	X
ejpam-4830	81	2	0	0	NUM
ejpam-4830	81	3	,	,	PUNCT
ejpam-4830	81	4	t−t	t−t	X
ejpam-4830	81	5	]	]	PUNCT
ejpam-4830	81	6	ofx	ofx	NOUN
ejpam-4830	81	7	and	and	CCONJ
ejpam-4830	81	8	ẽt	ẽt	NOUN
ejpam-4830	81	9	,	,	PUNCT
ejpam-4830	81	10	x	x	PRON
ejpam-4830	81	11	is	be	AUX
ejpam-4830	81	12	taken	take	VERB
ejpam-4830	81	13	with	with	ADP
ejpam-4830	81	14	respect	respect	NOUN
ejpam-4830	81	15	to	to	ADP
ejpam-4830	81	16	the	the	DET
ejpam-4830	81	17	(	(	PUNCT
ejpam-4830	81	18	unique	unique	ADJ
ejpam-4830	81	19	)	)	PUNCT
ejpam-4830	81	20	equivalent	equivalent	ADJ
ejpam-4830	81	21	martingale	martingale	NOUN
ejpam-4830	81	22	measure	measure	NOUN
ejpam-4830	81	23	p̃t	p̃t	NOUN
ejpam-4830	81	24	,	,	PUNCT
ejpam-4830	81	25	x	x	VERB
ejpam-4830	81	26	under	under	ADP
ejpam-4830	81	27	which	which	PRON
ejpam-4830	81	28	xt	xt	ADP
ejpam-4830	82	1	=	=	SYM
ejpam-4830	82	2	x	x	SYM
ejpam-4830	82	3	∈	∈	PROPN
ejpam-4830	82	4	r+	r+	NOUN
ejpam-4830	82	5	.	.	PUNCT
ejpam-4830	83	1	using	use	VERB
ejpam-4830	83	2	the	the	DET
ejpam-4830	83	3	same	same	ADJ
ejpam-4830	83	4	argument	argument	NOUN
ejpam-4830	83	5	as	as	ADP
ejpam-4830	83	6	above	above	ADV
ejpam-4830	83	7	with	with	ADP
ejpam-4830	83	8	µc	µc	VERB
ejpam-4830	83	9	is	be	AUX
ejpam-4830	83	10	replaced	replace	VERB
ejpam-4830	83	11	with	with	ADP
ejpam-4830	83	12	r	r	NOUN
ejpam-4830	83	13	in	in	ADP
ejpam-4830	83	14	relations	relation	NOUN
ejpam-4830	83	15	(	(	PUNCT
ejpam-4830	83	16	2	2	NUM
ejpam-4830	83	17	)	)	PUNCT
ejpam-4830	83	18	through	through	ADP
ejpam-4830	83	19	(	(	PUNCT
ejpam-4830	83	20	7	7	NUM
ejpam-4830	83	21	)	)	PUNCT
ejpam-4830	83	22	and	and	CCONJ
ejpam-4830	83	23	that	that	SCONJ
ejpam-4830	83	24	zr	zr	PROPN
ejpam-4830	83	25	t	t	PROPN
ejpam-4830	83	26	,	,	PUNCT
ejpam-4830	83	27	t+τ	t+τ	NUM
ejpam-4830	83	28	(	(	PUNCT
ejpam-4830	83	29	as	as	SCONJ
ejpam-4830	83	30	defined	define	VERB
ejpam-4830	83	31	in	in	ADP
ejpam-4830	83	32	(	(	PUNCT
ejpam-4830	83	33	11	11	NUM
ejpam-4830	83	34	)	)	PUNCT
ejpam-4830	83	35	with	with	ADP
ejpam-4830	83	36	µc	µc	ADV
ejpam-4830	83	37	is	be	AUX
ejpam-4830	83	38	replaced	replace	VERB
ejpam-4830	83	39	with	with	ADP
ejpam-4830	83	40	r	r	NOUN
ejpam-4830	83	41	)	)	PUNCT
ejpam-4830	83	42	has	have	VERB
ejpam-4830	83	43	stationary	stationary	ADJ
ejpam-4830	83	44	and	and	CCONJ
ejpam-4830	83	45	independent	independent	ADJ
ejpam-4830	83	46	increments	increment	NOUN
ejpam-4830	83	47	(	(	PUNCT
ejpam-4830	83	48	i.e.	i.e.	X
ejpam-4830	83	49	,	,	PUNCT
ejpam-4830	83	50	zr	zr	PROPN
ejpam-4830	83	51	t	t	PROPN
ejpam-4830	83	52	,	,	PUNCT
ejpam-4830	83	53	t+τ	t+τ	NUM
ejpam-4830	83	54	is	be	AUX
ejpam-4830	83	55	a	a	DET
ejpam-4830	83	56	version	version	NOUN
ejpam-4830	83	57	of	of	ADP
ejpam-4830	83	58	zr	zr	PROPN
ejpam-4830	83	59	0,τ	0,τ	PROPN
ejpam-4830	83	60	)	)	PUNCT
ejpam-4830	83	61	,	,	PUNCT
ejpam-4830	83	62	the	the	DET
ejpam-4830	83	63	option	option	NOUN
ejpam-4830	83	64	price	price	NOUN
ejpam-4830	83	65	in	in	ADP
ejpam-4830	83	66	(	(	PUNCT
ejpam-4830	83	67	15	15	NUM
ejpam-4830	83	68	)	)	PUNCT
ejpam-4830	83	69	can	can	AUX
ejpam-4830	83	70	be	be	AUX
ejpam-4830	83	71	f.	f.	PROPN
ejpam-4830	83	72	sumalpong	sumalpong	PROPN
ejpam-4830	83	73	,	,	PUNCT
ejpam-4830	83	74	m.	m.	PROPN
ejpam-4830	83	75	frondoza	frondoza	PROPN
ejpam-4830	83	76	,	,	PUNCT
ejpam-4830	83	77	n.l	n.l	PROPN
ejpam-4830	83	78	.	.	PROPN
ejpam-4830	83	79	sayson	sayson	PROPN
ejpam-4830	83	80	/	/	SYM
ejpam-4830	83	81	eur	eur	PROPN
ejpam-4830	83	82	.	.	PUNCT
ejpam-4830	84	1	j.	j.	PROPN
ejpam-4830	84	2	pure	pure	PROPN
ejpam-4830	84	3	appl	appl	PROPN
ejpam-4830	84	4	.	.	PROPN
ejpam-4830	84	5	math	math	PROPN
ejpam-4830	84	6	,	,	PUNCT
ejpam-4830	84	7	16	16	NUM
ejpam-4830	84	8	(	(	PUNCT
ejpam-4830	84	9	3	3	NUM
ejpam-4830	84	10	)	)	PUNCT
ejpam-4830	84	11	(	(	PUNCT
ejpam-4830	84	12	2023	2023	NUM
ejpam-4830	84	13	)	)	PUNCT
ejpam-4830	84	14	,	,	PUNCT
ejpam-4830	84	15	1830	1830	NUM
ejpam-4830	84	16	-	-	SYM
ejpam-4830	84	17	1847	1847	NUM
ejpam-4830	84	18	1834	1834	NUM
ejpam-4830	84	19	rewritten	rewrite	VERB
ejpam-4830	84	20	as	as	ADP
ejpam-4830	84	21	v	v	NOUN
ejpam-4830	84	22	(	(	PUNCT
ejpam-4830	84	23	t	t	PROPN
ejpam-4830	84	24	,	,	PUNCT
ejpam-4830	84	25	xt	xt	PROPN
ejpam-4830	84	26	,	,	PUNCT
ejpam-4830	84	27	αt	αt	NOUN
ejpam-4830	84	28	)	)	PUNCT
ejpam-4830	84	29	=	=	PUNCT
ejpam-4830	85	1	sup	sup	NOUN
ejpam-4830	85	2	0≤τ≤t−t	0≤τ≤t−t	NUM
ejpam-4830	85	3	e	e	NOUN
ejpam-4830	85	4	[	[	PUNCT
ejpam-4830	85	5	e−rτgµc(t+	e−rτgµc(t+	PROPN
ejpam-4830	85	6	τ	τ	PROPN
ejpam-4830	85	7	,	,	PUNCT
ejpam-4830	85	8	xtxτ	xtxτ	PROPN
ejpam-4830	85	9	,	,	PUNCT
ejpam-4830	85	10	j	j	PROPN
ejpam-4830	85	11	)	)	PUNCT
ejpam-4830	85	12	|	|	ADV
ejpam-4830	85	13	ft	ft	X
ejpam-4830	85	14	]	]	PUNCT
ejpam-4830	85	15	(	(	PUNCT
ejpam-4830	85	16	16	16	NUM
ejpam-4830	85	17	)	)	PUNCT
ejpam-4830	85	18	where	where	SCONJ
ejpam-4830	85	19	the	the	DET
ejpam-4830	85	20	process	process	NOUN
ejpam-4830	85	21	x	x	X
ejpam-4830	85	22	=	=	PUNCT
ejpam-4830	85	23	x(r	x(r	PROPN
ejpam-4830	85	24	)	)	PUNCT
ejpam-4830	85	25	under	under	ADP
ejpam-4830	85	26	p	p	NOUN
ejpam-4830	85	27	solves	solve	NOUN
ejpam-4830	86	1	dxt	dxt	PROPN
ejpam-4830	86	2	=	=	PUNCT
ejpam-4830	86	3	rxtdt+	rxtdt+	X
ejpam-4830	86	4	σ(αt)xtdw	σ(αt)xtdw	NOUN
ejpam-4830	86	5	r	r	NOUN
ejpam-4830	86	6	t	t	NOUN
ejpam-4830	86	7	with	with	ADP
ejpam-4830	86	8	x0	x0	PROPN
ejpam-4830	86	9	=	=	SYM
ejpam-4830	87	1	1	1	X
ejpam-4830	87	2	.	.	X
ejpam-4830	87	3	note	note	VERB
ejpam-4830	87	4	that	that	SCONJ
ejpam-4830	87	5	they	they	PRON
ejpam-4830	87	6	are	be	AUX
ejpam-4830	87	7	equivalent	equivalent	ADJ
ejpam-4830	87	8	because	because	SCONJ
ejpam-4830	87	9	ft	ft	PROPN
ejpam-4830	87	10	knows	know	VERB
ejpam-4830	87	11	the	the	DET
ejpam-4830	87	12	values	value	NOUN
ejpam-4830	87	13	of	of	ADP
ejpam-4830	87	14	xt	xt	PROPN
ejpam-4830	87	15	and	and	CCONJ
ejpam-4830	87	16	αt	αt	PROPN
ejpam-4830	87	17	.	.	PROPN
ejpam-4830	87	18	proposition	proposition	NOUN
ejpam-4830	87	19	1	1	NUM
ejpam-4830	87	20	.	.	X
ejpam-4830	88	1	for	for	ADP
ejpam-4830	88	2	any	any	DET
ejpam-4830	88	3	t	t	NOUN
ejpam-4830	88	4	∈	∈	PROPN
ejpam-4830	89	1	[	[	X
ejpam-4830	89	2	0	0	NUM
ejpam-4830	89	3	,	,	PUNCT
ejpam-4830	89	4	t	t	NOUN
ejpam-4830	89	5	]	]	PUNCT
ejpam-4830	89	6	and	and	CCONJ
ejpam-4830	89	7	j	j	PROPN
ejpam-4830	89	8	∈	∈	PROPN
ejpam-4830	89	9	m	m	AUX
ejpam-4830	89	10	given	give	VERB
ejpam-4830	89	11	and	and	CCONJ
ejpam-4830	89	12	fixed	fix	VERB
ejpam-4830	89	13	,	,	PUNCT
ejpam-4830	89	14	the	the	DET
ejpam-4830	89	15	mapping	mapping	NOUN
ejpam-4830	89	16	x	x	SYM
ejpam-4830	89	17	7→	7→	NUM
ejpam-4830	89	18	gµc(t	gµc(t	NOUN
ejpam-4830	89	19	,	,	PUNCT
ejpam-4830	89	20	x	x	NOUN
ejpam-4830	89	21	,	,	PUNCT
ejpam-4830	89	22	j	j	PROPN
ejpam-4830	89	23	)	)	PUNCT
ejpam-4830	89	24	(	(	PUNCT
ejpam-4830	89	25	17	17	NUM
ejpam-4830	89	26	)	)	PUNCT
ejpam-4830	89	27	is	be	AUX
ejpam-4830	89	28	convex	convex	ADJ
ejpam-4830	89	29	on	on	ADP
ejpam-4830	89	30	(	(	PUNCT
ejpam-4830	89	31	0,∞	0,∞	NUM
ejpam-4830	89	32	)	)	PUNCT
ejpam-4830	89	33	.	.	PUNCT
ejpam-4830	90	1	proof	proof	NOUN
ejpam-4830	90	2	.	.	PUNCT
ejpam-4830	91	1	let	let	VERB
ejpam-4830	91	2	0	0	NUM
ejpam-4830	91	3	≤	≤	NUM
ejpam-4830	92	1	λ	λ	X
ejpam-4830	92	2	≤	≤	NUM
ejpam-4830	92	3	1	1	NUM
ejpam-4830	92	4	and	and	CCONJ
ejpam-4830	92	5	x2	x2	PRON
ejpam-4830	92	6	=	=	PUNCT
ejpam-4830	92	7	λx1	λx1	X
ejpam-4830	93	1	+	+	PUNCT
ejpam-4830	93	2	(	(	PUNCT
ejpam-4830	93	3	1−	1−	NUM
ejpam-4830	93	4	λ)x3	λ)x3	PROPN
ejpam-4830	93	5	for	for	ADP
ejpam-4830	93	6	some	some	DET
ejpam-4830	93	7	x1	x1	PROPN
ejpam-4830	93	8	,	,	PUNCT
ejpam-4830	93	9	x3	x3	PROPN
ejpam-4830	93	10	∈	∈	PROPN
ejpam-4830	93	11	(	(	PUNCT
ejpam-4830	93	12	0,∞	0,∞	NOUN
ejpam-4830	93	13	)	)	PUNCT
ejpam-4830	93	14	with	with	ADP
ejpam-4830	93	15	x1	x1	PROPN
ejpam-4830	93	16	<	<	X
ejpam-4830	93	17	x3	x3	PROPN
ejpam-4830	93	18	.	.	PUNCT
ejpam-4830	94	1	we	we	PRON
ejpam-4830	94	2	have	have	VERB
ejpam-4830	94	3	gµc(t	gµc(t	PROPN
ejpam-4830	94	4	,	,	PUNCT
ejpam-4830	94	5	x2	x2	PROPN
ejpam-4830	94	6	,	,	PUNCT
ejpam-4830	94	7	j	j	PROPN
ejpam-4830	94	8	)	)	PUNCT
ejpam-4830	94	9	=	=	SYM
ejpam-4830	94	10	gµc(t	gµc(t	PROPN
ejpam-4830	94	11	,	,	PUNCT
ejpam-4830	94	12	λx1	λx1	X
ejpam-4830	94	13	+	+	CCONJ
ejpam-4830	94	14	(	(	PUNCT
ejpam-4830	94	15	1−	1−	NUM
ejpam-4830	94	16	λ)x3	λ)x3	PROPN
ejpam-4830	94	17	,	,	PUNCT
ejpam-4830	94	18	j	j	NOUN
ejpam-4830	94	19	)	)	PUNCT
ejpam-4830	94	20	=	=	PUNCT
ejpam-4830	95	1	eµc	eµc	PROPN
ejpam-4830	96	1	[	[	X
ejpam-4830	96	2	(	(	PUNCT
ejpam-4830	96	3	k	k	X
ejpam-4830	96	4	−	−	PROPN
ejpam-4830	96	5	λx1z	λx1z	INTJ
ejpam-4830	96	6	µc	µc	INTJ
ejpam-4830	96	7	t	t	PROPN
ejpam-4830	96	8	,	,	PUNCT
ejpam-4830	96	9	t	t	PROPN
ejpam-4830	96	10	−	−	PROPN
ejpam-4830	96	11	(	(	PUNCT
ejpam-4830	96	12	1−	1−	NUM
ejpam-4830	96	13	λ)x3z	λ)x3z	PROPN
ejpam-4830	96	14	µc	µc	PROPN
ejpam-4830	96	15	t	t	PROPN
ejpam-4830	96	16	,	,	PUNCT
ejpam-4830	96	17	t	t	PROPN
ejpam-4830	96	18	)	)	PUNCT
ejpam-4830	96	19	+	+	CCONJ
ejpam-4830	96	20	∣∣	∣∣	NUM
ejpam-4830	96	21	xt	xt	X
ejpam-4830	96	22	=	=	SYM
ejpam-4830	96	23	x	x	PROPN
ejpam-4830	96	24	,	,	PUNCT
ejpam-4830	96	25	αt	αt	PROPN
ejpam-4830	96	26	=	=	SYM
ejpam-4830	96	27	j	j	PROPN
ejpam-4830	96	28	]	]	X
ejpam-4830	96	29	=	=	PUNCT
ejpam-4830	97	1	eµc	eµc	PROPN
ejpam-4830	98	1	[	[	X
ejpam-4830	98	2	(	(	PUNCT
ejpam-4830	98	3	λk	λk	X
ejpam-4830	98	4	+	+	CCONJ
ejpam-4830	98	5	(	(	PUNCT
ejpam-4830	98	6	1−	1−	NUM
ejpam-4830	98	7	λ)k	λ)k	ADV
ejpam-4830	98	8	−	−	PROPN
ejpam-4830	99	1	λx1z	λx1z	INTJ
ejpam-4830	99	2	µc	µc	INTJ
ejpam-4830	99	3	t	t	PROPN
ejpam-4830	99	4	,	,	PUNCT
ejpam-4830	99	5	t	t	PROPN
ejpam-4830	99	6	−	−	PROPN
ejpam-4830	99	7	(	(	PUNCT
ejpam-4830	99	8	1−	1−	NUM
ejpam-4830	99	9	λ)x3z	λ)x3z	PROPN
ejpam-4830	99	10	µc	µc	PROPN
ejpam-4830	99	11	t	t	PROPN
ejpam-4830	99	12	,	,	PUNCT
ejpam-4830	99	13	t	t	PROPN
ejpam-4830	99	14	)	)	PUNCT
ejpam-4830	100	1	+	+	CCONJ
ejpam-4830	100	2	∣∣	∣∣	NUM
ejpam-4830	100	3	xt	xt	X
ejpam-4830	101	1	=	=	SYM
ejpam-4830	101	2	x	x	PROPN
ejpam-4830	101	3	,	,	PUNCT
ejpam-4830	101	4	αt	αt	PROPN
ejpam-4830	101	5	=	=	SYM
ejpam-4830	101	6	j	j	PROPN
ejpam-4830	101	7	]	]	PUNCT
ejpam-4830	101	8	≤	≤	NUM
ejpam-4830	102	1	λeµc	λeµc	NOUN
ejpam-4830	102	2	[	[	X
ejpam-4830	102	3	(	(	PUNCT
ejpam-4830	102	4	k	k	X
ejpam-4830	102	5	−	−	PROPN
ejpam-4830	102	6	x1z	x1z	PROPN
ejpam-4830	102	7	µc	µc	PROPN
ejpam-4830	102	8	t	t	PROPN
ejpam-4830	102	9	,	,	PUNCT
ejpam-4830	102	10	t	t	PROPN
ejpam-4830	102	11	)	)	PUNCT
ejpam-4830	103	1	+	+	CCONJ
ejpam-4830	103	2	∣∣	∣∣	NUM
ejpam-4830	103	3	xt	xt	X
ejpam-4830	104	1	=	=	SYM
ejpam-4830	104	2	x	x	PROPN
ejpam-4830	104	3	,	,	PUNCT
ejpam-4830	104	4	αt	αt	PROPN
ejpam-4830	104	5	=	=	SYM
ejpam-4830	104	6	j	j	PROPN
ejpam-4830	104	7	]	]	PUNCT
ejpam-4830	105	1	+	+	CCONJ
ejpam-4830	105	2	(	(	PUNCT
ejpam-4830	105	3	1−	1−	NUM
ejpam-4830	105	4	λ)eµc	λ)eµc	X
ejpam-4830	105	5	[	[	X
ejpam-4830	105	6	(	(	PUNCT
ejpam-4830	105	7	k	k	NOUN
ejpam-4830	105	8	−	−	PROPN
ejpam-4830	105	9	x3z	x3z	PROPN
ejpam-4830	105	10	µc	µc	PROPN
ejpam-4830	105	11	t	t	PROPN
ejpam-4830	105	12	,	,	PUNCT
ejpam-4830	105	13	t	t	PROPN
ejpam-4830	105	14	)	)	PUNCT
ejpam-4830	105	15	+	+	CCONJ
ejpam-4830	105	16	∣∣	∣∣	NUM
ejpam-4830	105	17	xt	xt	X
ejpam-4830	106	1	=	=	SYM
ejpam-4830	106	2	x	x	PROPN
ejpam-4830	106	3	,	,	PUNCT
ejpam-4830	106	4	αt	αt	PROPN
ejpam-4830	106	5	=	=	SYM
ejpam-4830	106	6	j	j	PROPN
ejpam-4830	106	7	]	]	X
ejpam-4830	106	8	=	=	SYM
ejpam-4830	106	9	λgµc(t	λgµc(t	PROPN
ejpam-4830	106	10	,	,	PUNCT
ejpam-4830	106	11	x1	x1	PROPN
ejpam-4830	106	12	,	,	PUNCT
ejpam-4830	106	13	j	j	NOUN
ejpam-4830	106	14	)	)	PUNCT
ejpam-4830	107	1	+	+	CCONJ
ejpam-4830	107	2	(	(	PUNCT
ejpam-4830	107	3	1−	1−	NUM
ejpam-4830	107	4	λ)gµc(t	λ)gµc(t	NOUN
ejpam-4830	107	5	,	,	PUNCT
ejpam-4830	107	6	x3	x3	ADJ
ejpam-4830	107	7	,	,	PUNCT
ejpam-4830	107	8	j	j	PROPN
ejpam-4830	107	9	)	)	PUNCT
ejpam-4830	107	10	,	,	PUNCT
ejpam-4830	107	11	which	which	PRON
ejpam-4830	107	12	completes	complete	VERB
ejpam-4830	107	13	our	our	PRON
ejpam-4830	107	14	proof	proof	NOUN
ejpam-4830	107	15	.	.	PUNCT
ejpam-4830	108	1	it	it	PRON
ejpam-4830	108	2	can	can	AUX
ejpam-4830	108	3	also	also	ADV
ejpam-4830	108	4	be	be	AUX
ejpam-4830	108	5	verified	verify	VERB
ejpam-4830	108	6	that	that	SCONJ
ejpam-4830	108	7	the	the	DET
ejpam-4830	108	8	mapping	mapping	NOUN
ejpam-4830	108	9	in	in	ADP
ejpam-4830	108	10	(	(	PUNCT
ejpam-4830	108	11	17	17	NUM
ejpam-4830	108	12	)	)	PUNCT
ejpam-4830	108	13	is	be	AUX
ejpam-4830	108	14	strictly	strictly	ADV
ejpam-4830	108	15	decreasing	decrease	VERB
ejpam-4830	108	16	on	on	ADP
ejpam-4830	108	17	(	(	PUNCT
ejpam-4830	108	18	0,∞	0,∞	NOUN
ejpam-4830	108	19	)	)	PUNCT
ejpam-4830	108	20	with	with	ADP
ejpam-4830	108	21	gµc(t	gµc(t	PROPN
ejpam-4830	108	22	,	,	PUNCT
ejpam-4830	108	23	x	x	NOUN
ejpam-4830	108	24	,	,	PUNCT
ejpam-4830	108	25	j	j	NOUN
ejpam-4830	108	26	)	)	PUNCT
ejpam-4830	108	27	=	=	PUNCT
ejpam-4830	109	1	(	(	PUNCT
ejpam-4830	109	2	k	k	NOUN
ejpam-4830	109	3	−xt	−xt	PROPN
ejpam-4830	109	4	)	)	PUNCT
ejpam-4830	110	1	+	+	ADJ
ejpam-4830	110	2	,	,	PUNCT
ejpam-4830	110	3	gµc(t	gµc(t	PROPN
ejpam-4830	110	4	,	,	PUNCT
ejpam-4830	110	5	0	0	NUM
ejpam-4830	110	6	,	,	PUNCT
ejpam-4830	110	7	j	j	NOUN
ejpam-4830	110	8	)	)	PUNCT
ejpam-4830	111	1	=	=	SYM
ejpam-4830	111	2	k	k	PROPN
ejpam-4830	111	3	and	and	CCONJ
ejpam-4830	111	4	lim	lim	PROPN
ejpam-4830	111	5	x→+∞	x→+∞	PROPN
ejpam-4830	111	6	gµc(t	gµc(t	PROPN
ejpam-4830	111	7	,	,	PUNCT
ejpam-4830	111	8	x	x	NOUN
ejpam-4830	111	9	,	,	PUNCT
ejpam-4830	111	10	j	j	NOUN
ejpam-4830	111	11	)	)	PUNCT
ejpam-4830	111	12	=	=	SYM
ejpam-4830	112	1	0	0	X
ejpam-4830	112	2	.	.	PUNCT
ejpam-4830	113	1	by	by	ADP
ejpam-4830	113	2	proposition	proposition	NOUN
ejpam-4830	113	3	1	1	NUM
ejpam-4830	113	4	and	and	CCONJ
ejpam-4830	113	5	equation	equation	NOUN
ejpam-4830	113	6	(	(	PUNCT
ejpam-4830	113	7	15	15	NUM
ejpam-4830	113	8	)	)	PUNCT
ejpam-4830	113	9	above	above	ADV
ejpam-4830	113	10	,	,	PUNCT
ejpam-4830	113	11	it	it	PRON
ejpam-4830	113	12	follows	follow	VERB
ejpam-4830	113	13	that	that	SCONJ
ejpam-4830	113	14	the	the	DET
ejpam-4830	113	15	mapping	mapping	NOUN
ejpam-4830	113	16	x	x	SYM
ejpam-4830	113	17	7→	7→	NUM
ejpam-4830	113	18	v	v	NOUN
ejpam-4830	113	19	(	(	PUNCT
ejpam-4830	113	20	t	t	PROPN
ejpam-4830	113	21	,	,	PUNCT
ejpam-4830	113	22	x	x	X
ejpam-4830	113	23	,	,	PUNCT
ejpam-4830	113	24	i	i	PROPN
ejpam-4830	113	25	)	)	PUNCT
ejpam-4830	113	26	(	(	PUNCT
ejpam-4830	113	27	18	18	NUM
ejpam-4830	113	28	)	)	PUNCT
ejpam-4830	113	29	is	be	AUX
ejpam-4830	113	30	convex	convex	ADJ
ejpam-4830	113	31	for	for	ADP
ejpam-4830	113	32	any	any	DET
ejpam-4830	113	33	t	t	NOUN
ejpam-4830	113	34	∈	∈	PROPN
ejpam-4830	114	1	[	[	X
ejpam-4830	114	2	0	0	NUM
ejpam-4830	114	3	,	,	PUNCT
ejpam-4830	114	4	t	t	NOUN
ejpam-4830	114	5	]	]	PUNCT
ejpam-4830	114	6	and	and	CCONJ
ejpam-4830	114	7	i	i	PRON
ejpam-4830	114	8	∈	∈	PROPN
ejpam-4830	114	9	m	m	AUX
ejpam-4830	114	10	given	give	VERB
ejpam-4830	114	11	and	and	CCONJ
ejpam-4830	114	12	fixed	fix	VERB
ejpam-4830	114	13	and	and	CCONJ
ejpam-4830	114	14	strictly	strictly	ADV
ejpam-4830	114	15	decreasing	decrease	VERB
ejpam-4830	114	16	on	on	ADP
ejpam-4830	114	17	(	(	PUNCT
ejpam-4830	114	18	0,∞	0,∞	NOUN
ejpam-4830	114	19	)	)	PUNCT
ejpam-4830	114	20	with	with	ADP
ejpam-4830	114	21	v	v	PROPN
ejpam-4830	114	22	(	(	PUNCT
ejpam-4830	114	23	t	t	PROPN
ejpam-4830	114	24	,	,	PUNCT
ejpam-4830	114	25	x	x	X
ejpam-4830	114	26	,	,	PUNCT
ejpam-4830	114	27	i	i	NOUN
ejpam-4830	114	28	)	)	PUNCT
ejpam-4830	114	29	=	=	SYM
ejpam-4830	115	1	(	(	PUNCT
ejpam-4830	115	2	k	k	PROPN
ejpam-4830	115	3	−	−	PROPN
ejpam-4830	115	4	xt	xt	PROPN
ejpam-4830	115	5	)	)	PUNCT
ejpam-4830	116	1	+	+	ADV
ejpam-4830	116	2	,	,	PUNCT
ejpam-4830	116	3	v	v	INTJ
ejpam-4830	116	4	(	(	PUNCT
ejpam-4830	116	5	t	t	PROPN
ejpam-4830	116	6	,	,	PUNCT
ejpam-4830	116	7	0	0	NUM
ejpam-4830	116	8	,	,	PUNCT
ejpam-4830	116	9	i	i	NOUN
ejpam-4830	116	10	)	)	PUNCT
ejpam-4830	117	1	=	=	SYM
ejpam-4830	117	2	k	k	PROPN
ejpam-4830	117	3	and	and	CCONJ
ejpam-4830	117	4	lim	lim	PROPN
ejpam-4830	117	5	x→+∞	x→+∞	PROPN
ejpam-4830	117	6	v	v	PROPN
ejpam-4830	117	7	(	(	PUNCT
ejpam-4830	117	8	t	t	PROPN
ejpam-4830	117	9	,	,	PUNCT
ejpam-4830	117	10	x	x	X
ejpam-4830	117	11	,	,	PUNCT
ejpam-4830	117	12	i	i	NOUN
ejpam-4830	117	13	)	)	PUNCT
ejpam-4830	118	1	=	=	PUNCT
ejpam-4830	118	2	0	0	X
ejpam-4830	118	3	.	.	PUNCT
ejpam-4830	119	1	hence	hence	ADV
ejpam-4830	119	2	,	,	PUNCT
ejpam-4830	119	3	both	both	DET
ejpam-4830	119	4	mappings	mapping	NOUN
ejpam-4830	119	5	(	(	PUNCT
ejpam-4830	119	6	17	17	NUM
ejpam-4830	119	7	)	)	PUNCT
ejpam-4830	119	8	and	and	CCONJ
ejpam-4830	119	9	(	(	PUNCT
ejpam-4830	119	10	18	18	NUM
ejpam-4830	119	11	)	)	PUNCT
ejpam-4830	119	12	are	be	AUX
ejpam-4830	119	13	continuous	continuous	ADJ
ejpam-4830	119	14	on	on	ADP
ejpam-4830	119	15	(	(	PUNCT
ejpam-4830	119	16	0,∞	0,∞	NOUN
ejpam-4830	119	17	)	)	PUNCT
ejpam-4830	119	18	for	for	ADP
ejpam-4830	119	19	any	any	DET
ejpam-4830	119	20	t	t	NOUN
ejpam-4830	119	21	∈	∈	PROPN
ejpam-4830	120	1	[	[	X
ejpam-4830	120	2	0	0	NUM
ejpam-4830	120	3	,	,	PUNCT
ejpam-4830	120	4	t	t	NOUN
ejpam-4830	120	5	]	]	PUNCT
ejpam-4830	120	6	and	and	CCONJ
ejpam-4830	120	7	αt	αt	PROPN
ejpam-4830	120	8	∈	∈	PROPN
ejpam-4830	120	9	m	m	AUX
ejpam-4830	120	10	given	give	VERB
ejpam-4830	120	11	and	and	CCONJ
ejpam-4830	120	12	fixed	fix	VERB
ejpam-4830	120	13	.	.	PUNCT
ejpam-4830	121	1	define	define	VERB
ejpam-4830	121	2	the	the	DET
ejpam-4830	121	3	set	set	NOUN
ejpam-4830	121	4	d	d	NOUN
ejpam-4830	121	5	:	:	PUNCT
ejpam-4830	121	6	=	=	SYM
ejpam-4830	121	7	{	{	PUNCT
ejpam-4830	121	8	(	(	PUNCT
ejpam-4830	121	9	t	t	PROPN
ejpam-4830	121	10	,	,	PUNCT
ejpam-4830	121	11	x	x	PROPN
ejpam-4830	121	12	,	,	PUNCT
ejpam-4830	121	13	j	j	NOUN
ejpam-4830	121	14	)	)	PUNCT
ejpam-4830	121	15	∈	∈	PROPN
ejpam-4830	122	1	[	[	X
ejpam-4830	122	2	0	0	NUM
ejpam-4830	122	3	,	,	PUNCT
ejpam-4830	122	4	t	t	X
ejpam-4830	122	5	]	]	X
ejpam-4830	122	6	×	×	NOUN
ejpam-4830	122	7	(	(	PUNCT
ejpam-4830	122	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	122	9	:	:	PUNCT
ejpam-4830	122	10	v	v	NUM
ejpam-4830	122	11	(	(	PUNCT
ejpam-4830	122	12	t	t	PROPN
ejpam-4830	122	13	,	,	PUNCT
ejpam-4830	122	14	x	x	NOUN
ejpam-4830	122	15	,	,	PUNCT
ejpam-4830	122	16	j	j	NOUN
ejpam-4830	122	17	)	)	PUNCT
ejpam-4830	122	18	=	=	SYM
ejpam-4830	122	19	gµc(t	gµc(t	PROPN
ejpam-4830	122	20	,	,	PUNCT
ejpam-4830	122	21	x	x	NOUN
ejpam-4830	122	22	,	,	PUNCT
ejpam-4830	122	23	j	j	NOUN
ejpam-4830	122	24	)	)	PUNCT
ejpam-4830	122	25	}	}	PUNCT
ejpam-4830	122	26	.	.	PUNCT
ejpam-4830	123	1	(	(	PUNCT
ejpam-4830	123	2	19	19	NUM
ejpam-4830	123	3	)	)	PUNCT
ejpam-4830	123	4	f.	f.	PROPN
ejpam-4830	123	5	sumalpong	sumalpong	PROPN
ejpam-4830	123	6	,	,	PUNCT
ejpam-4830	123	7	m.	m.	PROPN
ejpam-4830	123	8	frondoza	frondoza	PROPN
ejpam-4830	123	9	,	,	PUNCT
ejpam-4830	123	10	n.l	n.l	PROPN
ejpam-4830	123	11	.	.	PROPN
ejpam-4830	123	12	sayson	sayson	PROPN
ejpam-4830	123	13	/	/	SYM
ejpam-4830	123	14	eur	eur	PROPN
ejpam-4830	123	15	.	.	PUNCT
ejpam-4830	124	1	j.	j.	PROPN
ejpam-4830	124	2	pure	pure	PROPN
ejpam-4830	124	3	appl	appl	PROPN
ejpam-4830	124	4	.	.	PROPN
ejpam-4830	124	5	math	math	PROPN
ejpam-4830	124	6	,	,	PUNCT
ejpam-4830	124	7	16	16	NUM
ejpam-4830	124	8	(	(	PUNCT
ejpam-4830	124	9	3	3	NUM
ejpam-4830	124	10	)	)	PUNCT
ejpam-4830	124	11	(	(	PUNCT
ejpam-4830	124	12	2023	2023	NUM
ejpam-4830	124	13	)	)	PUNCT
ejpam-4830	124	14	,	,	PUNCT
ejpam-4830	124	15	1830	1830	NUM
ejpam-4830	124	16	-	-	SYM
ejpam-4830	124	17	1847	1847	NUM
ejpam-4830	124	18	1835	1835	NUM
ejpam-4830	124	19	let	let	VERB
ejpam-4830	124	20	(	(	PUNCT
ejpam-4830	124	21	t	t	PROPN
ejpam-4830	124	22	,	,	PUNCT
ejpam-4830	124	23	x	x	PROPN
ejpam-4830	124	24	,	,	PUNCT
ejpam-4830	124	25	j	j	PROPN
ejpam-4830	124	26	)	)	PUNCT
ejpam-4830	124	27	∈	∈	PROPN
ejpam-4830	124	28	{	{	PUNCT
ejpam-4830	124	29	t	t	PROPN
ejpam-4830	124	30	}	}	PUNCT
ejpam-4830	124	31	×	×	NOUN
ejpam-4830	124	32	(	(	PUNCT
ejpam-4830	124	33	0,∞)×m	0,∞)×m	ADJ
ejpam-4830	124	34	.	.	PUNCT
ejpam-4830	125	1	we	we	PRON
ejpam-4830	125	2	note	note	VERB
ejpam-4830	125	3	that	that	SCONJ
ejpam-4830	125	4	v	v	INTJ
ejpam-4830	125	5	(	(	PUNCT
ejpam-4830	125	6	t	t	PROPN
ejpam-4830	125	7	,	,	PUNCT
ejpam-4830	125	8	xt	xt	PROPN
ejpam-4830	125	9	,	,	PUNCT
ejpam-4830	125	10	j	j	PROPN
ejpam-4830	125	11	)	)	PUNCT
ejpam-4830	125	12	=	=	PUNCT
ejpam-4830	126	1	(	(	PUNCT
ejpam-4830	126	2	k	k	NOUN
ejpam-4830	126	3	−xt	−xt	PROPN
ejpam-4830	126	4	)	)	PUNCT
ejpam-4830	127	1	+	+	CCONJ
ejpam-4830	127	2	=	=	SYM
ejpam-4830	127	3	gµc(t	gµc(t	PROPN
ejpam-4830	127	4	,	,	PUNCT
ejpam-4830	127	5	xt	xt	X
ejpam-4830	127	6	,	,	PUNCT
ejpam-4830	127	7	j	j	PROPN
ejpam-4830	127	8	)	)	PUNCT
ejpam-4830	127	9	.	.	PUNCT
ejpam-4830	128	1	(	(	PUNCT
ejpam-4830	128	2	20	20	NUM
ejpam-4830	128	3	)	)	PUNCT
ejpam-4830	128	4	hence	hence	ADV
ejpam-4830	128	5	,	,	PUNCT
ejpam-4830	128	6	{	{	PUNCT
ejpam-4830	128	7	t	t	NOUN
ejpam-4830	128	8	}	}	PUNCT
ejpam-4830	128	9	×	×	PROPN
ejpam-4830	128	10	(	(	PUNCT
ejpam-4830	128	11	0,∞	0,∞	NOUN
ejpam-4830	128	12	)	)	PUNCT
ejpam-4830	128	13	×	×	NOUN
ejpam-4830	128	14	m	m	NOUN
ejpam-4830	128	15	⊂	⊂	PROPN
ejpam-4830	129	1	d	d	NOUN
ejpam-4830	129	2	,	,	PUNCT
ejpam-4830	129	3	which	which	PRON
ejpam-4830	129	4	is	be	AUX
ejpam-4830	129	5	consistent	consistent	ADJ
ejpam-4830	129	6	with	with	ADP
ejpam-4830	129	7	the	the	DET
ejpam-4830	129	8	fact	fact	NOUN
ejpam-4830	129	9	that	that	SCONJ
ejpam-4830	129	10	the	the	DET
ejpam-4830	129	11	supremum	supremum	NOUN
ejpam-4830	129	12	in	in	ADP
ejpam-4830	129	13	(	(	PUNCT
ejpam-4830	129	14	15	15	NUM
ejpam-4830	129	15	)	)	PUNCT
ejpam-4830	129	16	is	be	AUX
ejpam-4830	129	17	taken	take	VERB
ejpam-4830	129	18	over	over	ADP
ejpam-4830	129	19	(	(	PUNCT
ejpam-4830	129	20	ft)t∈[0,t	ft)t∈[0,t	NOUN
ejpam-4830	129	21	]	]	X
ejpam-4830	129	22	-stopping	-stopping	NOUN
ejpam-4830	129	23	times	time	NOUN
ejpam-4830	129	24	τ	τ	PROPN
ejpam-4830	129	25	∈	∈	PROPN
ejpam-4830	130	1	[	[	X
ejpam-4830	130	2	t	t	PROPN
ejpam-4830	130	3	,	,	PUNCT
ejpam-4830	130	4	t	t	X
ejpam-4830	130	5	]	]	PUNCT
ejpam-4830	130	6	.	.	PUNCT
ejpam-4830	131	1	furthermore	furthermore	ADV
ejpam-4830	131	2	,	,	PUNCT
ejpam-4830	131	3	by	by	ADP
ejpam-4830	131	4	corollary	corollary	ADJ
ejpam-4830	131	5	2.9	2.9	NUM
ejpam-4830	131	6	page	page	NOUN
ejpam-4830	131	7	46	46	NUM
ejpam-4830	131	8	in	in	ADP
ejpam-4830	131	9	peskir	peskir	NOUN
ejpam-4830	131	10	and	and	CCONJ
ejpam-4830	131	11	shiryaev	shiryaev	VERB
ejpam-4830	132	1	[	[	X
ejpam-4830	132	2	6	6	NUM
ejpam-4830	132	3	]	]	PUNCT
ejpam-4830	132	4	,	,	PUNCT
ejpam-4830	132	5	the	the	DET
ejpam-4830	132	6	(	(	PUNCT
ejpam-4830	132	7	ft)t∈[0,t	ft)t∈[0,t	NOUN
ejpam-4830	132	8	]	]	X
ejpam-4830	132	9	-stopping	-stopping	NOUN
ejpam-4830	132	10	time	time	NOUN
ejpam-4830	132	11	τd(t	τd(t	PUNCT
ejpam-4830	132	12	,	,	PUNCT
ejpam-4830	132	13	xt	xt	PROPN
ejpam-4830	132	14	,	,	PUNCT
ejpam-4830	132	15	αt	αt	NOUN
ejpam-4830	132	16	)	)	PUNCT
ejpam-4830	132	17	:	:	PUNCT
ejpam-4830	132	18	=	=	SYM
ejpam-4830	132	19	inf	inf	PROPN
ejpam-4830	132	20	{	{	PUNCT
ejpam-4830	132	21	s	s	NOUN
ejpam-4830	132	22	∈	∈	X
ejpam-4830	133	1	[	[	X
ejpam-4830	133	2	0	0	NUM
ejpam-4830	133	3	,	,	PUNCT
ejpam-4830	133	4	t	t	PROPN
ejpam-4830	133	5	−	−	PROPN
ejpam-4830	133	6	t	t	PROPN
ejpam-4830	133	7	]	]	PUNCT
ejpam-4830	133	8	:	:	PUNCT
ejpam-4830	133	9	(	(	PUNCT
ejpam-4830	133	10	t	t	PROPN
ejpam-4830	133	11	,	,	PUNCT
ejpam-4830	133	12	x	x	PROPN
ejpam-4830	133	13	,	,	PUNCT
ejpam-4830	133	14	j	j	NOUN
ejpam-4830	133	15	)	)	PUNCT
ejpam-4830	133	16	∈	∈	PROPN
ejpam-4830	134	1	d	d	NOUN
ejpam-4830	134	2	}	}	PUNCT
ejpam-4830	134	3	(	(	PUNCT
ejpam-4830	134	4	21	21	NUM
ejpam-4830	134	5	)	)	PUNCT
ejpam-4830	134	6	with	with	ADP
ejpam-4830	134	7	xt	xt	PROPN
ejpam-4830	134	8	=	=	SYM
ejpam-4830	134	9	x	x	SYM
ejpam-4830	134	10	∈	∈	PROPN
ejpam-4830	134	11	(	(	PUNCT
ejpam-4830	134	12	0,∞	0,∞	NOUN
ejpam-4830	134	13	)	)	PUNCT
ejpam-4830	134	14	and	and	CCONJ
ejpam-4830	134	15	αt	αt	NOUN
ejpam-4830	134	16	=	=	SYM
ejpam-4830	134	17	j	j	PROPN
ejpam-4830	134	18	∈	∈	PROPN
ejpam-4830	134	19	m	m	PROPN
ejpam-4830	134	20	,	,	PUNCT
ejpam-4830	134	21	is	be	AUX
ejpam-4830	134	22	an	an	DET
ejpam-4830	134	23	optimal	optimal	ADJ
ejpam-4830	134	24	stopping	stopping	NOUN
ejpam-4830	134	25	time	time	NOUN
ejpam-4830	134	26	for	for	ADP
ejpam-4830	134	27	option	option	NOUN
ejpam-4830	134	28	price	price	NOUN
ejpam-4830	134	29	in	in	ADP
ejpam-4830	134	30	(	(	PUNCT
ejpam-4830	134	31	15	15	NUM
ejpam-4830	134	32	)	)	PUNCT
ejpam-4830	134	33	since	since	SCONJ
ejpam-4830	134	34	x	x	PROPN
ejpam-4830	134	35	7→	7→	NUM
ejpam-4830	134	36	v	v	NOUN
ejpam-4830	134	37	(	(	PUNCT
ejpam-4830	134	38	t	t	PROPN
ejpam-4830	134	39	,	,	PUNCT
ejpam-4830	134	40	x	x	NOUN
ejpam-4830	134	41	,	,	PUNCT
ejpam-4830	134	42	j	j	PROPN
ejpam-4830	134	43	)	)	PUNCT
ejpam-4830	134	44	and	and	CCONJ
ejpam-4830	134	45	x	x	SYM
ejpam-4830	134	46	7→	7→	NUM
ejpam-4830	134	47	gµc(t	gµc(t	NOUN
ejpam-4830	134	48	,	,	PUNCT
ejpam-4830	134	49	x	x	NOUN
ejpam-4830	134	50	,	,	PUNCT
ejpam-4830	134	51	j	j	NOUN
ejpam-4830	134	52	)	)	PUNCT
ejpam-4830	134	53	are	be	AUX
ejpam-4830	134	54	both	both	ADV
ejpam-4830	134	55	continuous	continuous	ADJ
ejpam-4830	134	56	on	on	ADP
ejpam-4830	134	57	(	(	PUNCT
ejpam-4830	134	58	0,∞	0,∞	NOUN
ejpam-4830	134	59	)	)	PUNCT
ejpam-4830	134	60	and	and	CCONJ
ejpam-4830	134	61	gµc(t	gµc(t	NOUN
ejpam-4830	134	62	,	,	PUNCT
ejpam-4830	134	63	x	x	NOUN
ejpam-4830	134	64	,	,	PUNCT
ejpam-4830	134	65	j	j	NOUN
ejpam-4830	134	66	)	)	PUNCT
ejpam-4830	134	67	≤	≤	PUNCT
ejpam-4830	135	1	k	k	NOUN
ejpam-4830	135	2	for	for	ADP
ejpam-4830	135	3	all	all	DET
ejpam-4830	135	4	t	t	NOUN
ejpam-4830	135	5	∈	∈	PROPN
ejpam-4830	136	1	[	[	X
ejpam-4830	136	2	0	0	NUM
ejpam-4830	136	3	,	,	PUNCT
ejpam-4830	136	4	t	t	NOUN
ejpam-4830	136	5	]	]	PUNCT
ejpam-4830	136	6	and	and	CCONJ
ejpam-4830	136	7	j	j	PROPN
ejpam-4830	136	8	∈	∈	PROPN
ejpam-4830	136	9	m.	m.	NOUN
ejpam-4830	136	10	moreover	moreover	ADV
ejpam-4830	136	11	,	,	PUNCT
ejpam-4830	136	12	by	by	ADP
ejpam-4830	136	13	using	use	VERB
ejpam-4830	136	14	the	the	DET
ejpam-4830	136	15	equivalent	equivalent	ADJ
ejpam-4830	136	16	expression	expression	NOUN
ejpam-4830	136	17	for	for	ADP
ejpam-4830	136	18	the	the	DET
ejpam-4830	136	19	stopping	stopping	NOUN
ejpam-4830	136	20	set	set	VERB
ejpam-4830	136	21	d	d	NOUN
ejpam-4830	136	22	in	in	ADP
ejpam-4830	136	23	relation	relation	NOUN
ejpam-4830	136	24	(	(	PUNCT
ejpam-4830	136	25	46	46	NUM
ejpam-4830	136	26	)	)	PUNCT
ejpam-4830	136	27	in	in	ADP
ejpam-4830	136	28	proposition	proposition	NOUN
ejpam-4830	136	29	(	(	PUNCT
ejpam-4830	136	30	2	2	NUM
ejpam-4830	136	31	)	)	PUNCT
ejpam-4830	136	32	,	,	PUNCT
ejpam-4830	136	33	τd(t	τd(t	ADJ
ejpam-4830	136	34	,	,	PUNCT
ejpam-4830	136	35	xt	xt	PROPN
ejpam-4830	136	36	,	,	PUNCT
ejpam-4830	136	37	αt	αt	NOUN
ejpam-4830	136	38	)	)	PUNCT
ejpam-4830	136	39	can	can	AUX
ejpam-4830	136	40	be	be	AUX
ejpam-4830	136	41	rewritten	rewrite	VERB
ejpam-4830	136	42	in	in	ADP
ejpam-4830	136	43	terms	term	NOUN
ejpam-4830	136	44	of	of	ADP
ejpam-4830	136	45	the	the	DET
ejpam-4830	136	46	optimal	optimal	ADJ
ejpam-4830	136	47	stopping	stopping	NOUN
ejpam-4830	136	48	boundary	boundary	ADJ
ejpam-4830	136	49	function	function	NOUN
ejpam-4830	136	50	as	as	ADP
ejpam-4830	136	51	τd(t	τd(t	NOUN
ejpam-4830	136	52	,	,	PUNCT
ejpam-4830	136	53	x	x	X
ejpam-4830	136	54	,	,	PUNCT
ejpam-4830	136	55	j	j	PROPN
ejpam-4830	136	56	)	)	PUNCT
ejpam-4830	136	57	:	:	PUNCT
ejpam-4830	136	58	=	=	SYM
ejpam-4830	136	59	inf	inf	PROPN
ejpam-4830	136	60	{	{	PUNCT
ejpam-4830	136	61	s	s	NOUN
ejpam-4830	136	62	∈	∈	X
ejpam-4830	136	63	[	[	X
ejpam-4830	136	64	0	0	NUM
ejpam-4830	136	65	,	,	PUNCT
ejpam-4830	136	66	t	t	PROPN
ejpam-4830	136	67	−	−	PROPN
ejpam-4830	136	68	t	t	PROPN
ejpam-4830	136	69	]	]	PUNCT
ejpam-4830	136	70	:	:	PUNCT
ejpam-4830	136	71	x	x	SYM
ejpam-4830	136	72	≤	≤	X
ejpam-4830	136	73	bd(t	bd(t	NOUN
ejpam-4830	136	74	,	,	PUNCT
ejpam-4830	136	75	j	j	NOUN
ejpam-4830	136	76	)	)	PUNCT
ejpam-4830	136	77	}	}	PUNCT
ejpam-4830	136	78	,	,	PUNCT
ejpam-4830	136	79	(	(	PUNCT
ejpam-4830	136	80	22	22	NUM
ejpam-4830	136	81	)	)	PUNCT
ejpam-4830	136	82	where	where	SCONJ
ejpam-4830	136	83	bd(t	bd(t	ADP
ejpam-4830	136	84	,	,	PUNCT
ejpam-4830	136	85	j	j	NOUN
ejpam-4830	136	86	)	)	PUNCT
ejpam-4830	136	87	is	be	AUX
ejpam-4830	136	88	defined	define	VERB
ejpam-4830	136	89	in	in	ADP
ejpam-4830	136	90	(	(	PUNCT
ejpam-4830	136	91	44	44	NUM
ejpam-4830	136	92	)	)	PUNCT
ejpam-4830	136	93	below	below	ADP
ejpam-4830	136	94	at	at	ADP
ejpam-4830	136	95	which	which	PRON
ejpam-4830	136	96	xt	xt	ADP
ejpam-4830	137	1	=	=	SYM
ejpam-4830	137	2	x	x	X
ejpam-4830	137	3	and	and	CCONJ
ejpam-4830	137	4	αt	αt	PROPN
ejpam-4830	137	5	=	=	PROPN
ejpam-4830	137	6	j.	j.	PROPN
ejpam-4830	137	7	we	we	PRON
ejpam-4830	137	8	next	next	ADV
ejpam-4830	137	9	derive	derive	VERB
ejpam-4830	137	10	the	the	DET
ejpam-4830	137	11	following	follow	VERB
ejpam-4830	137	12	continuity	continuity	NOUN
ejpam-4830	137	13	results	result	NOUN
ejpam-4830	137	14	to	to	PART
ejpam-4830	137	15	show	show	VERB
ejpam-4830	137	16	that	that	SCONJ
ejpam-4830	137	17	the	the	DET
ejpam-4830	137	18	set	set	NOUN
ejpam-4830	137	19	d	d	NOUN
ejpam-4830	137	20	in	in	ADP
ejpam-4830	137	21	(	(	PUNCT
ejpam-4830	137	22	24	24	NUM
ejpam-4830	137	23	)	)	PUNCT
ejpam-4830	137	24	is	be	AUX
ejpam-4830	137	25	closed	close	VERB
ejpam-4830	137	26	.	.	PUNCT
ejpam-4830	138	1	lemma	lemma	PROPN
ejpam-4830	138	2	1	1	NUM
ejpam-4830	138	3	.	.	PUNCT
ejpam-4830	139	1	the	the	DET
ejpam-4830	139	2	mapping	mapping	NOUN
ejpam-4830	139	3	(	(	PUNCT
ejpam-4830	139	4	t	t	PROPN
ejpam-4830	139	5	,	,	PUNCT
ejpam-4830	139	6	x	x	NOUN
ejpam-4830	139	7	)	)	PUNCT
ejpam-4830	139	8	7→	7→	PROPN
ejpam-4830	139	9	gµc(t	gµc(t	NOUN
ejpam-4830	139	10	,	,	PUNCT
ejpam-4830	139	11	x	x	NOUN
ejpam-4830	139	12	,	,	PUNCT
ejpam-4830	139	13	j	j	NOUN
ejpam-4830	139	14	)	)	PUNCT
ejpam-4830	139	15	is	be	AUX
ejpam-4830	139	16	jointly	jointly	ADV
ejpam-4830	139	17	continuous	continuous	ADJ
ejpam-4830	139	18	on	on	ADP
ejpam-4830	139	19	[	[	X
ejpam-4830	139	20	0	0	NUM
ejpam-4830	139	21	,	,	PUNCT
ejpam-4830	139	22	t	t	X
ejpam-4830	139	23	]	]	X
ejpam-4830	139	24	×	×	NOUN
ejpam-4830	139	25	(	(	PUNCT
ejpam-4830	139	26	0,∞	0,∞	NUM
ejpam-4830	139	27	)	)	PUNCT
ejpam-4830	139	28	.	.	PUNCT
ejpam-4830	140	1	proof	proof	NOUN
ejpam-4830	140	2	.	.	PUNCT
ejpam-4830	141	1	the	the	DET
ejpam-4830	141	2	continuity	continuity	NOUN
ejpam-4830	141	3	of	of	ADP
ejpam-4830	141	4	the	the	DET
ejpam-4830	141	5	mapping	mapping	NOUN
ejpam-4830	141	6	x	x	PUNCT
ejpam-4830	141	7	7→	7→	NUM
ejpam-4830	141	8	gµc(t	gµc(t	NOUN
ejpam-4830	141	9	,	,	PUNCT
ejpam-4830	141	10	x	x	NOUN
ejpam-4830	141	11	,	,	PUNCT
ejpam-4830	141	12	j	j	PROPN
ejpam-4830	141	13	)	)	PUNCT
ejpam-4830	141	14	follows	follow	VERB
ejpam-4830	141	15	from	from	ADP
ejpam-4830	141	16	the	the	DET
ejpam-4830	141	17	fact	fact	NOUN
ejpam-4830	141	18	that	that	SCONJ
ejpam-4830	141	19	gµc(t	gµc(t	PROPN
ejpam-4830	141	20	,	,	PUNCT
ejpam-4830	141	21	x	x	NOUN
ejpam-4830	141	22	,	,	PUNCT
ejpam-4830	141	23	j	j	NOUN
ejpam-4830	141	24	)	)	PUNCT
ejpam-4830	141	25	is	be	AUX
ejpam-4830	141	26	convex	convex	ADJ
ejpam-4830	141	27	with	with	ADP
ejpam-4830	141	28	respect	respect	NOUN
ejpam-4830	141	29	to	to	ADP
ejpam-4830	141	30	x	x	SYM
ejpam-4830	141	31	∈	∈	PROPN
ejpam-4830	141	32	(	(	PUNCT
ejpam-4830	141	33	0,∞	0,∞	NOUN
ejpam-4830	141	34	)	)	PUNCT
ejpam-4830	141	35	for	for	ADP
ejpam-4830	141	36	any	any	DET
ejpam-4830	141	37	time	time	NOUN
ejpam-4830	141	38	t	t	X
ejpam-4830	141	39	∈	∈	PROPN
ejpam-4830	142	1	[	[	X
ejpam-4830	142	2	0	0	NUM
ejpam-4830	142	3	,	,	PUNCT
ejpam-4830	142	4	t	t	NOUN
ejpam-4830	142	5	]	]	PUNCT
ejpam-4830	142	6	given	give	VERB
ejpam-4830	142	7	and	and	CCONJ
ejpam-4830	142	8	fixed	fix	VERB
ejpam-4830	142	9	.	.	PUNCT
ejpam-4830	143	1	it	it	PRON
ejpam-4830	143	2	remains	remain	VERB
ejpam-4830	143	3	to	to	PART
ejpam-4830	143	4	show	show	VERB
ejpam-4830	143	5	the	the	DET
ejpam-4830	143	6	uniform	uniform	ADJ
ejpam-4830	143	7	continuity	continuity	NOUN
ejpam-4830	143	8	of	of	ADP
ejpam-4830	143	9	the	the	DET
ejpam-4830	143	10	mapping	mapping	NOUN
ejpam-4830	143	11	t	t	PROPN
ejpam-4830	143	12	7→	7→	PROPN
ejpam-4830	143	13	gµc(t	gµc(t	PROPN
ejpam-4830	143	14	,	,	PUNCT
ejpam-4830	143	15	x	x	NOUN
ejpam-4830	143	16	,	,	PUNCT
ejpam-4830	143	17	j	j	PROPN
ejpam-4830	143	18	)	)	PUNCT
ejpam-4830	143	19	at	at	ADP
ejpam-4830	143	20	time	time	NOUN
ejpam-4830	144	1	t	t	PROPN
ejpam-4830	144	2	=	=	SYM
ejpam-4830	144	3	t1	t1	PROPN
ejpam-4830	144	4	.	.	PUNCT
ejpam-4830	145	1	let	let	VERB
ejpam-4830	145	2	x	x	X
ejpam-4830	145	3	∈	∈	PROPN
ejpam-4830	145	4	(	(	PUNCT
ejpam-4830	145	5	0,∞	0,∞	NOUN
ejpam-4830	145	6	)	)	PUNCT
ejpam-4830	145	7	be	be	AUX
ejpam-4830	145	8	given	give	VERB
ejpam-4830	145	9	and	and	CCONJ
ejpam-4830	145	10	fixed	fix	VERB
ejpam-4830	145	11	and	and	CCONJ
ejpam-4830	145	12	0	0	NUM
ejpam-4830	145	13	≤	≤	NUM
ejpam-4830	146	1	t1	t1	NOUN
ejpam-4830	146	2	<	<	X
ejpam-4830	146	3	t2	t2	PROPN
ejpam-4830	146	4	≤	≤	PROPN
ejpam-4830	146	5	t	t	PROPN
ejpam-4830	146	6	.	.	PUNCT
ejpam-4830	147	1	then	then	ADV
ejpam-4830	147	2	we	we	PRON
ejpam-4830	147	3	have	have	VERB
ejpam-4830	147	4	,	,	PUNCT
ejpam-4830	147	5	0	0	NUM
ejpam-4830	147	6	≤	≤	NUM
ejpam-4830	147	7	∣∣∣gµc(t2	∣∣∣gµc(t2	NOUN
ejpam-4830	147	8	,	,	PUNCT
ejpam-4830	147	9	x	x	NOUN
ejpam-4830	147	10	,	,	PUNCT
ejpam-4830	147	11	j)−gµc(t1	j)−gµc(t1	PROPN
ejpam-4830	147	12	,	,	PUNCT
ejpam-4830	147	13	x	x	NOUN
ejpam-4830	147	14	,	,	PUNCT
ejpam-4830	147	15	j	j	NOUN
ejpam-4830	147	16	)	)	PUNCT
ejpam-4830	147	17	∣∣∣	∣∣∣	ADJ
ejpam-4830	147	18	≤	≤	PUNCT
ejpam-4830	148	1	eµc	eµc	PROPN
ejpam-4830	148	2	[	[	X
ejpam-4830	148	3	∣∣∣(k	∣∣∣(k	PROPN
ejpam-4830	148	4	−	−	PROPN
ejpam-4830	148	5	xzµc	xzµc	PROPN
ejpam-4830	148	6	t2,t	t2,t	PROPN
ejpam-4830	148	7	)	)	PUNCT
ejpam-4830	149	1	+	+	CCONJ
ejpam-4830	149	2	−	−	PROPN
ejpam-4830	149	3	(	(	PUNCT
ejpam-4830	149	4	k	k	NOUN
ejpam-4830	149	5	−	−	PROPN
ejpam-4830	149	6	xzµc	xzµc	PROPN
ejpam-4830	150	1	t1,t	t1,t	PROPN
ejpam-4830	150	2	)	)	PUNCT
ejpam-4830	151	1	+	+	CCONJ
ejpam-4830	151	2	∣∣∣	∣∣∣	ADJ
ejpam-4830	151	3	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	151	4	ft2	ft2	NOUN
ejpam-4830	151	5	]	]	PUNCT
ejpam-4830	151	6	≤	≤	NUM
ejpam-4830	151	7	xeµc	xeµc	NOUN
ejpam-4830	152	1	[	[	X
ejpam-4830	152	2	∣∣∣(zµc	∣∣∣(zµc	ADP
ejpam-4830	152	3	t1,t	t1,t	PROPN
ejpam-4830	152	4	−	−	PROPN
ejpam-4830	152	5	zµc	zµc	NOUN
ejpam-4830	152	6	t2,t	t2,t	PROPN
ejpam-4830	152	7	)	)	PUNCT
ejpam-4830	152	8	+	+	CCONJ
ejpam-4830	152	9	∣∣∣	∣∣∣	ADJ
ejpam-4830	152	10	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	152	11	ft2	ft2	NOUN
ejpam-4830	152	12	]	]	PUNCT
ejpam-4830	153	1	=	=	PUNCT
ejpam-4830	153	2	xeµc	xeµc	NOUN
ejpam-4830	154	1	[	[	X
ejpam-4830	154	2	∣∣∣∣∣zµc	∣∣∣∣∣zµc	ADP
ejpam-4830	154	3	t1,t	t1,t	PROPN
ejpam-4830	154	4	(	(	PUNCT
ejpam-4830	154	5	1−	1−	NUM
ejpam-4830	154	6	zµc	zµc	NOUN
ejpam-4830	154	7	t2,t	t2,t	PROPN
ejpam-4830	154	8	zµc	zµc	ADP
ejpam-4830	154	9	t1,t	t1,t	PROPN
ejpam-4830	154	10	)	)	PUNCT
ejpam-4830	154	11	+	+	CCONJ
ejpam-4830	154	12	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	154	13	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4830	154	14	ft2	ft2	NOUN
ejpam-4830	154	15	]	]	PUNCT
ejpam-4830	154	16	=	=	PUNCT
ejpam-4830	154	17	xeµc	xeµc	NOUN
ejpam-4830	154	18	∣∣∣∣∣zµc	∣∣∣∣∣zµc	ADP
ejpam-4830	154	19	t1,t	t1,t	PROPN
ejpam-4830	154	20	(	(	PUNCT
ejpam-4830	154	21	1−	1−	NUM
ejpam-4830	154	22	e	e	NOUN
ejpam-4830	154	23	−	−	PROPN
ejpam-4830	154	24	∫	∫	PROPN
ejpam-4830	154	25	t2	t2	PROPN
ejpam-4830	154	26	t1	t1	PROPN
ejpam-4830	154	27	(	(	PUNCT
ejpam-4830	154	28	µc−σ2(αu	µc−σ2(αu	PROPN
ejpam-4830	154	29	)	)	PUNCT
ejpam-4830	154	30	2	2	NUM
ejpam-4830	154	31	)	)	PUNCT
ejpam-4830	154	32	du−	du−	NUM
ejpam-4830	154	33	∫	∫	PROPN
ejpam-4830	154	34	t2	t2	PROPN
ejpam-4830	154	35	t1	t1	PROPN
ejpam-4830	154	36	σ(αu)dw	σ(αu)dw	PROPN
ejpam-4830	154	37	µc	µc	PROPN
ejpam-4830	154	38	u	u	NOUN
ejpam-4830	154	39	)	)	PUNCT
ejpam-4830	154	40	+	+	CCONJ
ejpam-4830	154	41	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	154	42	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4830	154	43	ft2	ft2	NOUN
ejpam-4830	154	44			NOUN
ejpam-4830	154	45	.	.	PUNCT
ejpam-4830	155	1	therefore	therefore	ADV
ejpam-4830	155	2	,	,	PUNCT
ejpam-4830	155	3	as	as	ADP
ejpam-4830	155	4	t2	t2	PROPN
ejpam-4830	155	5	−	−	PROPN
ejpam-4830	155	6	t1	t1	PROPN
ejpam-4830	155	7	→	→	SYM
ejpam-4830	155	8	0	0	NUM
ejpam-4830	155	9	,	,	PUNCT
ejpam-4830	155	10	we	we	PRON
ejpam-4830	155	11	have	have	VERB
ejpam-4830	155	12	gµc(t2	gµc(t2	NOUN
ejpam-4830	155	13	,	,	PUNCT
ejpam-4830	155	14	x	x	NOUN
ejpam-4830	155	15	,	,	PUNCT
ejpam-4830	155	16	j	j	PROPN
ejpam-4830	155	17	)	)	PUNCT
ejpam-4830	155	18	−	−	PROPN
ejpam-4830	156	1	gµc(t1	gµc(t1	NOUN
ejpam-4830	156	2	,	,	PUNCT
ejpam-4830	156	3	x	x	NOUN
ejpam-4830	156	4	,	,	PUNCT
ejpam-4830	156	5	j	j	PROPN
ejpam-4830	156	6	)	)	PUNCT
ejpam-4830	156	7	→	→	SYM
ejpam-4830	156	8	0	0	NUM
ejpam-4830	156	9	uniformly	uniformly	ADV
ejpam-4830	156	10	,	,	PUNCT
ejpam-4830	156	11	which	which	PRON
ejpam-4830	156	12	completes	complete	VERB
ejpam-4830	156	13	our	our	PRON
ejpam-4830	156	14	proof	proof	NOUN
ejpam-4830	156	15	.	.	PUNCT
ejpam-4830	157	1	f.	f.	PROPN
ejpam-4830	157	2	sumalpong	sumalpong	PROPN
ejpam-4830	157	3	,	,	PUNCT
ejpam-4830	157	4	m.	m.	PROPN
ejpam-4830	157	5	frondoza	frondoza	PROPN
ejpam-4830	157	6	,	,	PUNCT
ejpam-4830	157	7	n.l	n.l	PROPN
ejpam-4830	157	8	.	.	PROPN
ejpam-4830	157	9	sayson	sayson	PROPN
ejpam-4830	157	10	/	/	SYM
ejpam-4830	157	11	eur	eur	PROPN
ejpam-4830	157	12	.	.	PUNCT
ejpam-4830	158	1	j.	j.	PROPN
ejpam-4830	158	2	pure	pure	PROPN
ejpam-4830	158	3	appl	appl	PROPN
ejpam-4830	158	4	.	.	PROPN
ejpam-4830	158	5	math	math	PROPN
ejpam-4830	158	6	,	,	PUNCT
ejpam-4830	158	7	16	16	NUM
ejpam-4830	158	8	(	(	PUNCT
ejpam-4830	158	9	3	3	NUM
ejpam-4830	158	10	)	)	PUNCT
ejpam-4830	158	11	(	(	PUNCT
ejpam-4830	158	12	2023	2023	NUM
ejpam-4830	158	13	)	)	PUNCT
ejpam-4830	158	14	,	,	PUNCT
ejpam-4830	158	15	1830	1830	NUM
ejpam-4830	158	16	-	-	SYM
ejpam-4830	158	17	1847	1847	NUM
ejpam-4830	158	18	1836	1836	NUM
ejpam-4830	158	19	lemma	lemma	PROPN
ejpam-4830	158	20	2	2	NUM
ejpam-4830	158	21	.	.	X
ejpam-4830	159	1	for	for	ADP
ejpam-4830	159	2	any	any	DET
ejpam-4830	159	3	j	j	PROPN
ejpam-4830	159	4	∈	∈	PROPN
ejpam-4830	159	5	m	m	PROPN
ejpam-4830	159	6	,	,	PUNCT
ejpam-4830	159	7	the	the	DET
ejpam-4830	159	8	mapping	mapping	NOUN
ejpam-4830	159	9	(	(	PUNCT
ejpam-4830	159	10	t	t	PROPN
ejpam-4830	159	11	,	,	PUNCT
ejpam-4830	159	12	x	x	NOUN
ejpam-4830	159	13	)	)	PUNCT
ejpam-4830	159	14	7→	7→	NUM
ejpam-4830	159	15	v	v	NOUN
ejpam-4830	159	16	(	(	PUNCT
ejpam-4830	159	17	t	t	PROPN
ejpam-4830	159	18	,	,	PUNCT
ejpam-4830	159	19	x	x	PROPN
ejpam-4830	159	20	,	,	PUNCT
ejpam-4830	159	21	j	j	NOUN
ejpam-4830	159	22	)	)	PUNCT
ejpam-4830	159	23	is	be	AUX
ejpam-4830	159	24	jointly	jointly	ADV
ejpam-4830	159	25	continuous	continuous	ADJ
ejpam-4830	159	26	on	on	ADP
ejpam-4830	159	27	[	[	X
ejpam-4830	159	28	0	0	NUM
ejpam-4830	159	29	,	,	PUNCT
ejpam-4830	159	30	t	t	X
ejpam-4830	159	31	]	]	X
ejpam-4830	159	32	×	×	NOUN
ejpam-4830	159	33	(	(	PUNCT
ejpam-4830	159	34	0,∞	0,∞	NUM
ejpam-4830	159	35	)	)	PUNCT
ejpam-4830	159	36	.	.	PUNCT
ejpam-4830	160	1	proof	proof	NOUN
ejpam-4830	160	2	.	.	PUNCT
ejpam-4830	161	1	the	the	DET
ejpam-4830	161	2	continuity	continuity	NOUN
ejpam-4830	161	3	of	of	ADP
ejpam-4830	161	4	the	the	DET
ejpam-4830	161	5	mapping	mapping	NOUN
ejpam-4830	161	6	x	x	SYM
ejpam-4830	161	7	7→	7→	NUM
ejpam-4830	161	8	v	v	NOUN
ejpam-4830	161	9	(	(	PUNCT
ejpam-4830	161	10	t	t	PROPN
ejpam-4830	161	11	,	,	PUNCT
ejpam-4830	161	12	x	x	NOUN
ejpam-4830	161	13	,	,	PUNCT
ejpam-4830	161	14	j	j	NOUN
ejpam-4830	161	15	)	)	PUNCT
ejpam-4830	161	16	at	at	ADP
ejpam-4830	161	17	a	a	DET
ejpam-4830	161	18	point	point	NOUN
ejpam-4830	161	19	x0	x0	PROPN
ejpam-4830	161	20	follows	follow	VERB
ejpam-4830	161	21	from	from	ADP
ejpam-4830	161	22	the	the	DET
ejpam-4830	161	23	fact	fact	NOUN
ejpam-4830	161	24	that	that	SCONJ
ejpam-4830	161	25	v	v	X
ejpam-4830	161	26	(	(	PUNCT
ejpam-4830	161	27	t	t	PROPN
ejpam-4830	161	28	,	,	PUNCT
ejpam-4830	161	29	x	x	PROPN
ejpam-4830	161	30	,	,	PUNCT
ejpam-4830	161	31	j	j	NOUN
ejpam-4830	161	32	)	)	PUNCT
ejpam-4830	161	33	is	be	AUX
ejpam-4830	161	34	convex	convex	ADJ
ejpam-4830	161	35	with	with	ADP
ejpam-4830	161	36	respect	respect	NOUN
ejpam-4830	161	37	to	to	ADP
ejpam-4830	161	38	x	x	SYM
ejpam-4830	161	39	∈	∈	PROPN
ejpam-4830	161	40	(	(	PUNCT
ejpam-4830	161	41	0,∞	0,∞	NOUN
ejpam-4830	161	42	)	)	PUNCT
ejpam-4830	161	43	for	for	ADP
ejpam-4830	161	44	any	any	DET
ejpam-4830	161	45	time	time	NOUN
ejpam-4830	161	46	t	t	X
ejpam-4830	161	47	∈	∈	PROPN
ejpam-4830	162	1	[	[	X
ejpam-4830	162	2	0	0	NUM
ejpam-4830	162	3	,	,	PUNCT
ejpam-4830	162	4	t	t	NOUN
ejpam-4830	162	5	]	]	PUNCT
ejpam-4830	162	6	given	give	VERB
ejpam-4830	162	7	and	and	CCONJ
ejpam-4830	162	8	fixed	fix	VERB
ejpam-4830	162	9	.	.	PUNCT
ejpam-4830	163	1	it	it	PRON
ejpam-4830	163	2	remains	remain	VERB
ejpam-4830	163	3	to	to	PART
ejpam-4830	163	4	show	show	VERB
ejpam-4830	163	5	that	that	SCONJ
ejpam-4830	163	6	the	the	DET
ejpam-4830	163	7	mapping	mapping	NOUN
ejpam-4830	163	8	t	t	NOUN
ejpam-4830	163	9	7→	7→	NUM
ejpam-4830	163	10	v	v	NOUN
ejpam-4830	163	11	(	(	PUNCT
ejpam-4830	163	12	t	t	PROPN
ejpam-4830	163	13	,	,	PUNCT
ejpam-4830	163	14	x	x	PROPN
ejpam-4830	163	15	,	,	PUNCT
ejpam-4830	163	16	j	j	NOUN
ejpam-4830	163	17	)	)	PUNCT
ejpam-4830	163	18	is	be	AUX
ejpam-4830	163	19	continuous	continuous	ADJ
ejpam-4830	163	20	at	at	ADP
ejpam-4830	163	21	t1	t1	NOUN
ejpam-4830	163	22	uniformly	uniformly	ADV
ejpam-4830	163	23	over	over	ADP
ejpam-4830	163	24	x	x	PROPN
ejpam-4830	163	25	∈	∈	PROPN
ejpam-4830	163	26	r.	r.	NOUN
ejpam-4830	163	27	let	let	VERB
ejpam-4830	163	28	x	x	X
ejpam-4830	163	29	∈	∈	PROPN
ejpam-4830	163	30	(	(	PUNCT
ejpam-4830	163	31	0,∞	0,∞	NOUN
ejpam-4830	163	32	)	)	PUNCT
ejpam-4830	163	33	be	be	AUX
ejpam-4830	163	34	given	give	VERB
ejpam-4830	163	35	and	and	CCONJ
ejpam-4830	163	36	fixed	fix	VERB
ejpam-4830	163	37	and	and	CCONJ
ejpam-4830	163	38	suppose	suppose	VERB
ejpam-4830	164	1	0	0	NUM
ejpam-4830	164	2	≤	≤	NUM
ejpam-4830	164	3	t1	t1	NOUN
ejpam-4830	164	4	<	<	X
ejpam-4830	164	5	t2	t2	PROPN
ejpam-4830	164	6	≤	≤	PROPN
ejpam-4830	164	7	t	t	PROPN
ejpam-4830	164	8	.	.	PUNCT
ejpam-4830	165	1	let	let	VERB
ejpam-4830	165	2	τ1	τ1	NOUN
ejpam-4830	165	3	=	=	SYM
ejpam-4830	165	4	τd(t	τd(t	X
ejpam-4830	165	5	,	,	PUNCT
ejpam-4830	165	6	x	x	PRON
ejpam-4830	165	7	,	,	PUNCT
ejpam-4830	165	8	i	i	PRON
ejpam-4830	165	9	)	)	PUNCT
ejpam-4830	165	10	be	be	VERB
ejpam-4830	165	11	the	the	DET
ejpam-4830	165	12	optimal	optimal	ADJ
ejpam-4830	165	13	stopping	stopping	NOUN
ejpam-4830	165	14	time	time	NOUN
ejpam-4830	165	15	for	for	ADP
ejpam-4830	165	16	(	(	PUNCT
ejpam-4830	165	17	15	15	NUM
ejpam-4830	165	18	)	)	PUNCT
ejpam-4830	165	19	and	and	CCONJ
ejpam-4830	165	20	τ2	τ2	NOUN
ejpam-4830	165	21	=	=	SYM
ejpam-4830	165	22	τ1	τ1	NOUN
ejpam-4830	165	23	∧	∧	PROPN
ejpam-4830	165	24	(	(	PUNCT
ejpam-4830	165	25	t	t	NOUN
ejpam-4830	165	26	−	−	PROPN
ejpam-4830	165	27	t2	t2	PROPN
ejpam-4830	165	28	)	)	PUNCT
ejpam-4830	165	29	.	.	PUNCT
ejpam-4830	166	1	then	then	ADV
ejpam-4830	166	2	0	0	NUM
ejpam-4830	166	3	≤	≤	ADJ
ejpam-4830	166	4	∣∣∣v	∣∣∣v	NOUN
ejpam-4830	166	5	(	(	PUNCT
ejpam-4830	166	6	t1	t1	PROPN
ejpam-4830	166	7	,	,	PUNCT
ejpam-4830	166	8	x	x	PRON
ejpam-4830	166	9	,	,	PUNCT
ejpam-4830	166	10	i)−	i)−	PROPN
ejpam-4830	166	11	v	v	NOUN
ejpam-4830	166	12	(	(	PUNCT
ejpam-4830	166	13	t2	t2	NOUN
ejpam-4830	166	14	,	,	PUNCT
ejpam-4830	166	15	x	x	X
ejpam-4830	166	16	,	,	PUNCT
ejpam-4830	166	17	i	i	NOUN
ejpam-4830	166	18	)	)	PUNCT
ejpam-4830	166	19	∣∣∣	∣∣∣	ADP
ejpam-4830	166	20	≤	≤	NUM
ejpam-4830	167	1	∣∣∣e	∣∣∣e	PROPN
ejpam-4830	168	1	[	[	X
ejpam-4830	168	2	e−rτ1gµc(t1	e−rτ1gµc(t1	NOUN
ejpam-4830	168	3	+	+	CCONJ
ejpam-4830	168	4	τ1	τ1	NOUN
ejpam-4830	168	5	,	,	PUNCT
ejpam-4830	168	6	xt1+τ1	xt1+τ1	PROPN
ejpam-4830	168	7	,	,	PUNCT
ejpam-4830	168	8	j	j	PROPN
ejpam-4830	168	9	)	)	PUNCT
ejpam-4830	168	10	∣∣	∣∣	PROPN
ejpam-4830	168	11	ft1	ft1	X
ejpam-4830	168	12	]	]	PUNCT
ejpam-4830	168	13	−e	−e	NOUN
ejpam-4830	168	14	[	[	PUNCT
ejpam-4830	168	15	e−rτ2gµc(t2	e−rτ2gµc(t2	PROPN
ejpam-4830	168	16	+	+	X
ejpam-4830	168	17	τ2	τ2	ADJ
ejpam-4830	168	18	,	,	PUNCT
ejpam-4830	168	19	xt2+τ2	xt2+τ2	PROPN
ejpam-4830	168	20	,	,	PUNCT
ejpam-4830	168	21	j	j	PROPN
ejpam-4830	168	22	)	)	PUNCT
ejpam-4830	168	23	∣∣	∣∣	PROPN
ejpam-4830	168	24	ft2	ft2	PROPN
ejpam-4830	168	25	]	]	PUNCT
ejpam-4830	168	26	∣∣∣	∣∣∣	ADJ
ejpam-4830	168	27	≤	≤	NUM
ejpam-4830	168	28	∣∣∣e	∣∣∣e	PROPN
ejpam-4830	169	1	[	[	X
ejpam-4830	169	2	e−rτ2gµc(t1	e−rτ2gµc(t1	NOUN
ejpam-4830	169	3	+	+	CCONJ
ejpam-4830	169	4	τ1	τ1	NOUN
ejpam-4830	169	5	,	,	PUNCT
ejpam-4830	169	6	xt1+τ1	xt1+τ1	PROPN
ejpam-4830	169	7	,	,	PUNCT
ejpam-4830	169	8	j	j	PROPN
ejpam-4830	169	9	)	)	PUNCT
ejpam-4830	169	10	∣∣	∣∣	PROPN
ejpam-4830	169	11	ft1	ft1	X
ejpam-4830	169	12	]	]	PUNCT
ejpam-4830	169	13	−e	−e	NOUN
ejpam-4830	169	14	[	[	PUNCT
ejpam-4830	169	15	e−rτ2gµc(t2	e−rτ2gµc(t2	PROPN
ejpam-4830	169	16	+	+	X
ejpam-4830	169	17	τ2	τ2	ADJ
ejpam-4830	169	18	,	,	PUNCT
ejpam-4830	169	19	xt2+τ2	xt2+τ2	PROPN
ejpam-4830	169	20	,	,	PUNCT
ejpam-4830	169	21	j	j	PROPN
ejpam-4830	169	22	)	)	PUNCT
ejpam-4830	169	23	∣∣	∣∣	PROPN
ejpam-4830	169	24	ft2	ft2	PROPN
ejpam-4830	169	25	]	]	PUNCT
ejpam-4830	169	26	∣∣∣	∣∣∣	ADJ
ejpam-4830	169	27	≤	≤	NUM
ejpam-4830	169	28	∣∣∣e	∣∣∣e	PROPN
ejpam-4830	170	1	[	[	X
ejpam-4830	170	2	e−rτ2	e−rτ2	X
ejpam-4830	170	3	{	{	PUNCT
ejpam-4830	170	4	gµc(t1	gµc(t1	NOUN
ejpam-4830	170	5	+	+	CCONJ
ejpam-4830	170	6	τ1	τ1	NOUN
ejpam-4830	170	7	,	,	PUNCT
ejpam-4830	170	8	xt1+τ1	xt1+τ1	PROPN
ejpam-4830	170	9	,	,	PUNCT
ejpam-4830	170	10	j)−gµc(t2	j)−gµc(t2	PROPN
ejpam-4830	170	11	+	+	CCONJ
ejpam-4830	170	12	τ2	τ2	ADJ
ejpam-4830	170	13	,	,	PUNCT
ejpam-4830	170	14	xt2+τ2	xt2+τ2	PROPN
ejpam-4830	170	15	,	,	PUNCT
ejpam-4830	170	16	j	j	PROPN
ejpam-4830	170	17	)	)	PUNCT
ejpam-4830	170	18	}	}	PUNCT
ejpam-4830	170	19	∣∣	∣∣	PROPN
ejpam-4830	170	20	ft2	ft2	NOUN
ejpam-4830	170	21	]	]	PUNCT
ejpam-4830	170	22	∣∣∣	∣∣∣	ADJ
ejpam-4830	170	23	≤	≤	NUM
ejpam-4830	170	24	e	e	NOUN
ejpam-4830	170	25	[	[	PUNCT
ejpam-4830	170	26	e−rτ2	e−rτ2	X
ejpam-4830	170	27	∣∣gµc(t1	∣∣gµc(t1	VERB
ejpam-4830	170	28	+	+	CCONJ
ejpam-4830	170	29	τ1	τ1	NOUN
ejpam-4830	170	30	,	,	PUNCT
ejpam-4830	170	31	xt1+τ1	xt1+τ1	PROPN
ejpam-4830	170	32	,	,	PUNCT
ejpam-4830	170	33	j)−gµc(t2	j)−gµc(t2	PROPN
ejpam-4830	170	34	+	+	CCONJ
ejpam-4830	170	35	τ2	τ2	ADJ
ejpam-4830	170	36	,	,	PUNCT
ejpam-4830	170	37	xt2+τ2	xt2+τ2	PROPN
ejpam-4830	170	38	,	,	PUNCT
ejpam-4830	170	39	j	j	PROPN
ejpam-4830	170	40	)	)	PUNCT
ejpam-4830	170	41	∣∣	∣∣	X
ejpam-4830	170	42	∣∣∣	∣∣∣	ADP
ejpam-4830	170	43	ft2	ft2	PROPN
ejpam-4830	170	44	]	]	PUNCT
ejpam-4830	170	45	.	.	PUNCT
ejpam-4830	171	1	by	by	ADP
ejpam-4830	171	2	the	the	DET
ejpam-4830	171	3	continuity	continuity	NOUN
ejpam-4830	171	4	of	of	ADP
ejpam-4830	171	5	the	the	DET
ejpam-4830	171	6	mapping	mapping	NOUN
ejpam-4830	171	7	t	t	PROPN
ejpam-4830	171	8	7→	7→	PROPN
ejpam-4830	171	9	gµc(t	gµc(t	PROPN
ejpam-4830	171	10	,	,	PUNCT
ejpam-4830	171	11	x	x	NOUN
ejpam-4830	171	12	,	,	PUNCT
ejpam-4830	171	13	j	j	PROPN
ejpam-4830	171	14	)	)	PUNCT
ejpam-4830	171	15	from	from	ADP
ejpam-4830	171	16	lemma	lemma	PROPN
ejpam-4830	171	17	1	1	NUM
ejpam-4830	171	18	,	,	PUNCT
ejpam-4830	171	19	the	the	DET
ejpam-4830	171	20	mapping	mapping	NOUN
ejpam-4830	171	21	t	t	NOUN
ejpam-4830	171	22	7→	7→	NUM
ejpam-4830	171	23	v	v	NOUN
ejpam-4830	171	24	(	(	PUNCT
ejpam-4830	171	25	t	t	PROPN
ejpam-4830	171	26	,	,	PUNCT
ejpam-4830	171	27	x	x	X
ejpam-4830	171	28	,	,	PUNCT
ejpam-4830	171	29	i	i	PRON
ejpam-4830	171	30	)	)	PUNCT
ejpam-4830	171	31	is	be	AUX
ejpam-4830	171	32	continuous	continuous	ADJ
ejpam-4830	171	33	on	on	ADP
ejpam-4830	171	34	[	[	X
ejpam-4830	171	35	0	0	NUM
ejpam-4830	171	36	,	,	PUNCT
ejpam-4830	171	37	t	t	X
ejpam-4830	171	38	]	]	PUNCT
ejpam-4830	171	39	,	,	PUNCT
ejpam-4830	171	40	uniformly	uniformly	ADV
ejpam-4830	171	41	in	in	ADP
ejpam-4830	171	42	x	x	SYM
ejpam-4830	171	43	∈	∈	PROPN
ejpam-4830	171	44	(	(	PUNCT
ejpam-4830	171	45	0,∞	0,∞	NOUN
ejpam-4830	171	46	)	)	PUNCT
ejpam-4830	171	47	.	.	PUNCT
ejpam-4830	172	1	3	3	X
ejpam-4830	172	2	.	.	X
ejpam-4830	172	3	stopping	stop	VERB
ejpam-4830	172	4	set	set	VERB
ejpam-4830	172	5	and	and	CCONJ
ejpam-4830	172	6	boundary	boundary	ADJ
ejpam-4830	172	7	function	function	NOUN
ejpam-4830	172	8	define	define	VERB
ejpam-4830	172	9	f	f	PROPN
ejpam-4830	172	10	(	(	PUNCT
ejpam-4830	172	11	t	t	PROPN
ejpam-4830	172	12	,	,	PUNCT
ejpam-4830	172	13	x	x	PROPN
ejpam-4830	172	14	,	,	PUNCT
ejpam-4830	172	15	j	j	NOUN
ejpam-4830	172	16	)	)	PUNCT
ejpam-4830	173	1	=	=	SYM
ejpam-4830	173	2	v	v	X
ejpam-4830	173	3	(	(	PUNCT
ejpam-4830	173	4	t	t	PROPN
ejpam-4830	173	5	,	,	PUNCT
ejpam-4830	173	6	x	x	X
ejpam-4830	173	7	,	,	PUNCT
ejpam-4830	173	8	j)−g(t	j)−g(t	PROPN
ejpam-4830	173	9	,	,	PUNCT
ejpam-4830	173	10	x	x	PROPN
ejpam-4830	173	11	,	,	PUNCT
ejpam-4830	173	12	j	j	PROPN
ejpam-4830	173	13	)	)	PUNCT
ejpam-4830	173	14	≥	≥	NOUN
ejpam-4830	173	15	0	0	NUM
ejpam-4830	173	16	,	,	PUNCT
ejpam-4830	173	17	(	(	PUNCT
ejpam-4830	173	18	23	23	NUM
ejpam-4830	173	19	)	)	PUNCT
ejpam-4830	173	20	which	which	PRON
ejpam-4830	173	21	is	be	AUX
ejpam-4830	173	22	nonnegative	nonnegative	ADJ
ejpam-4830	173	23	for	for	ADP
ejpam-4830	173	24	t	t	PROPN
ejpam-4830	173	25	∈	∈	PROPN
ejpam-4830	174	1	[	[	X
ejpam-4830	174	2	0	0	NUM
ejpam-4830	174	3	,	,	PUNCT
ejpam-4830	174	4	t	t	X
ejpam-4830	174	5	]	]	PUNCT
ejpam-4830	174	6	,	,	PUNCT
ejpam-4830	174	7	x	x	SYM
ejpam-4830	174	8	∈	∈	PROPN
ejpam-4830	174	9	(	(	PUNCT
ejpam-4830	174	10	0,∞	0,∞	NOUN
ejpam-4830	174	11	)	)	PUNCT
ejpam-4830	174	12	and	and	CCONJ
ejpam-4830	174	13	j	j	PROPN
ejpam-4830	174	14	∈	∈	PROPN
ejpam-4830	174	15	m	m	PROPN
ejpam-4830	174	16	,	,	PUNCT
ejpam-4830	174	17	so	so	SCONJ
ejpam-4830	174	18	that	that	SCONJ
ejpam-4830	174	19	we	we	PRON
ejpam-4830	174	20	have	have	VERB
ejpam-4830	174	21	d	d	NOUN
ejpam-4830	174	22	=	=	PRON
ejpam-4830	174	23	{	{	PUNCT
ejpam-4830	174	24	(	(	PUNCT
ejpam-4830	174	25	t	t	PROPN
ejpam-4830	174	26	,	,	PUNCT
ejpam-4830	174	27	x	x	PROPN
ejpam-4830	174	28	,	,	PUNCT
ejpam-4830	174	29	j	j	NOUN
ejpam-4830	174	30	)	)	PUNCT
ejpam-4830	174	31	∈	∈	PROPN
ejpam-4830	175	1	[	[	X
ejpam-4830	175	2	0	0	NUM
ejpam-4830	175	3	,	,	PUNCT
ejpam-4830	175	4	t	t	X
ejpam-4830	175	5	]	]	X
ejpam-4830	175	6	×	×	NOUN
ejpam-4830	175	7	(	(	PUNCT
ejpam-4830	175	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	175	9	:	:	PUNCT
ejpam-4830	175	10	f	f	PROPN
ejpam-4830	175	11	(	(	PUNCT
ejpam-4830	175	12	t	t	PROPN
ejpam-4830	175	13	,	,	PUNCT
ejpam-4830	175	14	x	x	PROPN
ejpam-4830	175	15	,	,	PUNCT
ejpam-4830	175	16	j	j	NOUN
ejpam-4830	175	17	)	)	PUNCT
ejpam-4830	175	18	=	=	PUNCT
ejpam-4830	175	19	0	0	NUM
ejpam-4830	175	20	}	}	PUNCT
ejpam-4830	175	21	.	.	PUNCT
ejpam-4830	176	1	(	(	PUNCT
ejpam-4830	176	2	24	24	NUM
ejpam-4830	176	3	)	)	PUNCT
ejpam-4830	176	4	by	by	ADP
ejpam-4830	176	5	the	the	DET
ejpam-4830	176	6	continuity	continuity	NOUN
ejpam-4830	176	7	of	of	ADP
ejpam-4830	176	8	both	both	DET
ejpam-4830	176	9	mappings	mapping	NOUN
ejpam-4830	176	10	(	(	PUNCT
ejpam-4830	176	11	t	t	NOUN
ejpam-4830	176	12	,	,	PUNCT
ejpam-4830	176	13	x	x	NOUN
ejpam-4830	176	14	)	)	PUNCT
ejpam-4830	176	15	7→	7→	NUM
ejpam-4830	176	16	v	v	NOUN
ejpam-4830	176	17	(	(	PUNCT
ejpam-4830	176	18	t	t	PROPN
ejpam-4830	176	19	,	,	PUNCT
ejpam-4830	176	20	x	x	X
ejpam-4830	176	21	,	,	PUNCT
ejpam-4830	176	22	i	i	PROPN
ejpam-4830	176	23	)	)	PUNCT
ejpam-4830	176	24	and	and	CCONJ
ejpam-4830	176	25	(	(	PUNCT
ejpam-4830	176	26	t	t	PROPN
ejpam-4830	176	27	,	,	PUNCT
ejpam-4830	176	28	x	x	NOUN
ejpam-4830	176	29	)	)	PUNCT
ejpam-4830	176	30	7→	7→	PROPN
ejpam-4830	176	31	gµc(t	gµc(t	NOUN
ejpam-4830	176	32	,	,	PUNCT
ejpam-4830	176	33	x	x	NOUN
ejpam-4830	176	34	,	,	PUNCT
ejpam-4830	176	35	j	j	NOUN
ejpam-4830	176	36	)	)	PUNCT
ejpam-4830	176	37	on	on	ADP
ejpam-4830	176	38	[	[	X
ejpam-4830	176	39	0	0	NUM
ejpam-4830	176	40	,	,	PUNCT
ejpam-4830	176	41	t	t	X
ejpam-4830	176	42	]	]	X
ejpam-4830	176	43	×	×	NOUN
ejpam-4830	176	44	(	(	PUNCT
ejpam-4830	176	45	0,∞	0,∞	NUM
ejpam-4830	176	46	)	)	PUNCT
ejpam-4830	176	47	,	,	PUNCT
ejpam-4830	176	48	the	the	DET
ejpam-4830	176	49	set	set	NOUN
ejpam-4830	176	50	d	d	PROPN
ejpam-4830	176	51	is	be	AUX
ejpam-4830	176	52	closed	closed	ADJ
ejpam-4830	176	53	.	.	PUNCT
ejpam-4830	177	1	thus	thus	ADV
ejpam-4830	177	2	,	,	PUNCT
ejpam-4830	177	3	the	the	DET
ejpam-4830	177	4	continuation	continuation	NOUN
ejpam-4830	177	5	set	set	VERB
ejpam-4830	177	6	c	c	NOUN
ejpam-4830	177	7	=	=	SYM
ejpam-4830	177	8	dc	dc	PROPN
ejpam-4830	177	9	=	=	SYM
ejpam-4830	177	10	{	{	PUNCT
ejpam-4830	177	11	(	(	PUNCT
ejpam-4830	177	12	t	t	PROPN
ejpam-4830	177	13	,	,	PUNCT
ejpam-4830	177	14	x	x	PROPN
ejpam-4830	177	15	,	,	PUNCT
ejpam-4830	177	16	j	j	NOUN
ejpam-4830	177	17	)	)	PUNCT
ejpam-4830	177	18	∈	∈	PROPN
ejpam-4830	178	1	[	[	X
ejpam-4830	178	2	0	0	NUM
ejpam-4830	178	3	,	,	PUNCT
ejpam-4830	178	4	t	t	X
ejpam-4830	178	5	]	]	X
ejpam-4830	178	6	×	×	NOUN
ejpam-4830	178	7	(	(	PUNCT
ejpam-4830	178	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	178	9	:	:	PUNCT
ejpam-4830	178	10	f	f	PROPN
ejpam-4830	178	11	(	(	PUNCT
ejpam-4830	178	12	t	t	PROPN
ejpam-4830	178	13	,	,	PUNCT
ejpam-4830	178	14	x	x	PROPN
ejpam-4830	178	15	,	,	PUNCT
ejpam-4830	178	16	j	j	PROPN
ejpam-4830	178	17	)	)	PUNCT
ejpam-4830	178	18	>	>	X
ejpam-4830	178	19	0	0	NUM
ejpam-4830	178	20	}	}	PUNCT
ejpam-4830	178	21	(	(	PUNCT
ejpam-4830	178	22	25	25	NUM
ejpam-4830	178	23	)	)	PUNCT
ejpam-4830	178	24	is	be	AUX
ejpam-4830	178	25	open	open	ADJ
ejpam-4830	178	26	.	.	PUNCT
ejpam-4830	179	1	lemma	lemma	PROPN
ejpam-4830	179	2	3	3	NUM
ejpam-4830	179	3	.	.	X
ejpam-4830	180	1	for	for	ADP
ejpam-4830	180	2	any	any	DET
ejpam-4830	180	3	(	(	PUNCT
ejpam-4830	180	4	t	t	PROPN
ejpam-4830	180	5	,	,	PUNCT
ejpam-4830	180	6	x	x	NOUN
ejpam-4830	180	7	,	,	PUNCT
ejpam-4830	180	8	j	j	NOUN
ejpam-4830	180	9	)	)	PUNCT
ejpam-4830	180	10	∈	∈	PROPN
ejpam-4830	181	1	d	d	X
ejpam-4830	181	2	,	,	PUNCT
ejpam-4830	181	3	we	we	PRON
ejpam-4830	181	4	have	have	VERB
ejpam-4830	181	5	lim	lim	PROPN
ejpam-4830	181	6	sup	sup	PROPN
ejpam-4830	181	7	ϵ	ϵ	PROPN
ejpam-4830	181	8	↘	↘	PROPN
ejpam-4830	181	9	0	0	PROPN
ejpam-4830	181	10	f	f	PROPN
ejpam-4830	181	11	(	(	PUNCT
ejpam-4830	181	12	t	t	PROPN
ejpam-4830	181	13	,	,	PUNCT
ejpam-4830	181	14	x+	x+	PROPN
ejpam-4830	182	1	ϵ	ϵ	X
ejpam-4830	182	2	,	,	PUNCT
ejpam-4830	182	3	j)−	j)−	PROPN
ejpam-4830	182	4	f	f	PROPN
ejpam-4830	182	5	(	(	PUNCT
ejpam-4830	182	6	t	t	PROPN
ejpam-4830	182	7	,	,	PUNCT
ejpam-4830	182	8	x	x	PROPN
ejpam-4830	182	9	,	,	PUNCT
ejpam-4830	182	10	j	j	PROPN
ejpam-4830	182	11	)	)	PUNCT
ejpam-4830	182	12	ϵ	ϵ	ADP
ejpam-4830	182	13	≤	≤	NUM
ejpam-4830	182	14	0	0	NUM
ejpam-4830	182	15	.	.	PUNCT
ejpam-4830	183	1	(	(	PUNCT
ejpam-4830	183	2	26	26	NUM
ejpam-4830	183	3	)	)	PUNCT
ejpam-4830	183	4	f.	f.	PROPN
ejpam-4830	183	5	sumalpong	sumalpong	PROPN
ejpam-4830	183	6	,	,	PUNCT
ejpam-4830	183	7	m.	m.	PROPN
ejpam-4830	183	8	frondoza	frondoza	PROPN
ejpam-4830	183	9	,	,	PUNCT
ejpam-4830	183	10	n.l	n.l	PROPN
ejpam-4830	183	11	.	.	PROPN
ejpam-4830	183	12	sayson	sayson	PROPN
ejpam-4830	183	13	/	/	SYM
ejpam-4830	183	14	eur	eur	PROPN
ejpam-4830	183	15	.	.	PUNCT
ejpam-4830	184	1	j.	j.	PROPN
ejpam-4830	184	2	pure	pure	PROPN
ejpam-4830	184	3	appl	appl	PROPN
ejpam-4830	184	4	.	.	PROPN
ejpam-4830	184	5	math	math	PROPN
ejpam-4830	184	6	,	,	PUNCT
ejpam-4830	184	7	16	16	NUM
ejpam-4830	184	8	(	(	PUNCT
ejpam-4830	184	9	3	3	NUM
ejpam-4830	184	10	)	)	PUNCT
ejpam-4830	184	11	(	(	PUNCT
ejpam-4830	184	12	2023	2023	NUM
ejpam-4830	184	13	)	)	PUNCT
ejpam-4830	184	14	,	,	PUNCT
ejpam-4830	184	15	1830	1830	NUM
ejpam-4830	184	16	-	-	SYM
ejpam-4830	184	17	1847	1847	NUM
ejpam-4830	184	18	1837	1837	NUM
ejpam-4830	184	19	proof	proof	NOUN
ejpam-4830	184	20	.	.	PUNCT
ejpam-4830	185	1	for	for	ADP
ejpam-4830	185	2	all	all	DET
ejpam-4830	185	3	x	x	SYM
ejpam-4830	185	4	∈	∈	PROPN
ejpam-4830	185	5	(	(	PUNCT
ejpam-4830	185	6	0,∞	0,∞	NOUN
ejpam-4830	185	7	)	)	PUNCT
ejpam-4830	185	8	and	and	CCONJ
ejpam-4830	185	9	ϵ	ϵ	X
ejpam-4830	185	10	>	>	X
ejpam-4830	185	11	0	0	NUM
ejpam-4830	185	12	,	,	PUNCT
ejpam-4830	185	13	consider	consider	VERB
ejpam-4830	185	14	the	the	DET
ejpam-4830	185	15	(	(	PUNCT
ejpam-4830	185	16	fs)s∈[t	fs)s∈[t	PROPN
ejpam-4830	185	17	,	,	PUNCT
ejpam-4830	185	18	t	t	NOUN
ejpam-4830	185	19	]	]	PUNCT
ejpam-4830	185	20	-stopping	-stopping	NOUN
ejpam-4830	185	21	time	time	NOUN
ejpam-4830	185	22	τ+ϵ	τ+ϵ	X
ejpam-4830	185	23	=	=	SYM
ejpam-4830	185	24	τd(t	τd(t	X
ejpam-4830	185	25	,	,	PUNCT
ejpam-4830	185	26	x+	x+	ADJ
ejpam-4830	185	27	ϵ	ϵ	X
ejpam-4830	185	28	,	,	PUNCT
ejpam-4830	185	29	j	j	PROPN
ejpam-4830	185	30	)	)	PUNCT
ejpam-4830	185	31	∈	∈	PROPN
ejpam-4830	186	1	[	[	X
ejpam-4830	186	2	0	0	NUM
ejpam-4830	186	3	,	,	PUNCT
ejpam-4830	186	4	t	t	PROPN
ejpam-4830	186	5	−	−	PROPN
ejpam-4830	186	6	t	t	PROPN
ejpam-4830	186	7	]	]	PUNCT
ejpam-4830	186	8	(	(	PUNCT
ejpam-4830	186	9	27	27	NUM
ejpam-4830	186	10	)	)	PUNCT
ejpam-4830	186	11	defined	define	VERB
ejpam-4830	186	12	in	in	ADP
ejpam-4830	186	13	(	(	PUNCT
ejpam-4830	186	14	21	21	NUM
ejpam-4830	186	15	)	)	PUNCT
ejpam-4830	186	16	,	,	PUNCT
ejpam-4830	187	1	which	which	PRON
ejpam-4830	187	2	solves	solve	VERB
ejpam-4830	187	3	the	the	DET
ejpam-4830	187	4	optimal	optimal	ADJ
ejpam-4830	187	5	stopping	stopping	NOUN
ejpam-4830	187	6	problem	problem	NOUN
ejpam-4830	187	7	v	v	ADP
ejpam-4830	187	8	(	(	PUNCT
ejpam-4830	187	9	t	t	PROPN
ejpam-4830	187	10	,	,	PUNCT
ejpam-4830	187	11	x+	x+	PROPN
ejpam-4830	187	12	ϵ	ϵ	X
ejpam-4830	187	13	,	,	PUNCT
ejpam-4830	187	14	αt	αt	NOUN
ejpam-4830	187	15	)	)	PUNCT
ejpam-4830	187	16	=	=	PUNCT
ejpam-4830	187	17	sup	sup	NOUN
ejpam-4830	187	18	0≤τ≤t−t	0≤τ≤t−t	NUM
ejpam-4830	187	19	e	e	NOUN
ejpam-4830	187	20	[	[	PUNCT
ejpam-4830	187	21	e−rτgµc(t+	e−rτgµc(t+	PROPN
ejpam-4830	187	22	τ	τ	PROPN
ejpam-4830	187	23	,	,	PUNCT
ejpam-4830	187	24	xt+τ	xt+τ	PROPN
ejpam-4830	187	25	,	,	PUNCT
ejpam-4830	187	26	j	j	PROPN
ejpam-4830	187	27	)	)	PUNCT
ejpam-4830	187	28	∣∣∣ft	∣∣∣ft	PUNCT
ejpam-4830	187	29	]	]	PUNCT
ejpam-4830	188	1	=	=	PUNCT
ejpam-4830	188	2	e	e	X
ejpam-4830	188	3	[	[	PUNCT
ejpam-4830	188	4	e−rτ+ϵ	e−rτ+ϵ	NUM
ejpam-4830	188	5	gµc(t+	gµc(t+	NOUN
ejpam-4830	188	6	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	188	7	,	,	PUNCT
ejpam-4830	188	8	xt+τ+ϵ	xt+τ+ϵ	PROPN
ejpam-4830	188	9	,	,	PUNCT
ejpam-4830	188	10	j	j	PROPN
ejpam-4830	188	11	)	)	PUNCT
ejpam-4830	188	12	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	188	13	]	]	PUNCT
ejpam-4830	188	14	.	.	PUNCT
ejpam-4830	189	1	(	(	PUNCT
ejpam-4830	189	2	28	28	NUM
ejpam-4830	189	3	)	)	PUNCT
ejpam-4830	189	4	we	we	PRON
ejpam-4830	189	5	first	first	ADV
ejpam-4830	189	6	claim	claim	VERB
ejpam-4830	189	7	that	that	SCONJ
ejpam-4830	189	8	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	189	9	→	→	SYM
ejpam-4830	189	10	0	0	NUM
ejpam-4830	189	11	as	as	ADP
ejpam-4830	189	12	ϵ	ϵ	PROPN
ejpam-4830	189	13	→	→	SYM
ejpam-4830	189	14	0	0	NUM
ejpam-4830	189	15	.	.	PUNCT
ejpam-4830	190	1	(	(	PUNCT
ejpam-4830	190	2	29	29	NUM
ejpam-4830	190	3	)	)	PUNCT
ejpam-4830	190	4	from	from	ADP
ejpam-4830	190	5	the	the	DET
ejpam-4830	190	6	definition	definition	NOUN
ejpam-4830	190	7	of	of	ADP
ejpam-4830	190	8	τd(t	τd(t	DET
ejpam-4830	190	9	,	,	PUNCT
ejpam-4830	190	10	x+	x+	PROPN
ejpam-4830	190	11	ϵ	ϵ	X
ejpam-4830	190	12	,	,	PUNCT
ejpam-4830	190	13	j	j	PROPN
ejpam-4830	190	14	)	)	PUNCT
ejpam-4830	190	15	,	,	PUNCT
ejpam-4830	190	16	we	we	PRON
ejpam-4830	190	17	have	have	VERB
ejpam-4830	190	18	,	,	PUNCT
ejpam-4830	190	19	on	on	ADP
ejpam-4830	190	20	the	the	DET
ejpam-4830	190	21	event	event	NOUN
ejpam-4830	190	22	{	{	PUNCT
ejpam-4830	190	23	αt	αt	PROPN
ejpam-4830	190	24	=	=	SYM
ejpam-4830	190	25	j	j	PROPN
ejpam-4830	190	26	}	}	PUNCT
ejpam-4830	190	27	,	,	PUNCT
ejpam-4830	190	28	τd(t	τd(t	ADJ
ejpam-4830	190	29	,	,	PUNCT
ejpam-4830	190	30	x+	x+	ADJ
ejpam-4830	190	31	ϵ	ϵ	X
ejpam-4830	190	32	,	,	PUNCT
ejpam-4830	190	33	j	j	NOUN
ejpam-4830	190	34	)	)	PUNCT
ejpam-4830	190	35	=	=	SYM
ejpam-4830	190	36	inf	inf	NOUN
ejpam-4830	190	37	{	{	PUNCT
ejpam-4830	190	38	s	s	NOUN
ejpam-4830	190	39	∈	∈	X
ejpam-4830	191	1	[	[	X
ejpam-4830	191	2	0	0	NUM
ejpam-4830	191	3	,	,	PUNCT
ejpam-4830	191	4	t	t	PROPN
ejpam-4830	191	5	−	−	PROPN
ejpam-4830	191	6	t	t	PROPN
ejpam-4830	191	7	]	]	PUNCT
ejpam-4830	191	8	:	:	PUNCT
ejpam-4830	191	9	(	(	PUNCT
ejpam-4830	191	10	t	t	PROPN
ejpam-4830	191	11	,	,	PUNCT
ejpam-4830	191	12	x+	x+	PROPN
ejpam-4830	191	13	ϵ	ϵ	X
ejpam-4830	191	14	,	,	PUNCT
ejpam-4830	191	15	j	j	PROPN
ejpam-4830	191	16	)	)	PUNCT
ejpam-4830	191	17	∈	∈	PROPN
ejpam-4830	191	18	d	d	NOUN
ejpam-4830	191	19	}	}	PUNCT
ejpam-4830	191	20	=	=	SYM
ejpam-4830	191	21	inf	inf	NOUN
ejpam-4830	191	22	{	{	PUNCT
ejpam-4830	191	23	s	s	PROPN
ejpam-4830	191	24	∈	∈	PROPN
ejpam-4830	192	1	[	[	X
ejpam-4830	192	2	0	0	NUM
ejpam-4830	192	3	,	,	PUNCT
ejpam-4830	192	4	t	t	PROPN
ejpam-4830	192	5	−	−	PROPN
ejpam-4830	192	6	t	t	PROPN
ejpam-4830	192	7	]	]	PUNCT
ejpam-4830	192	8	:	:	PUNCT
ejpam-4830	192	9	sup	sup	NOUN
ejpam-4830	192	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	192	11	e	e	X
ejpam-4830	192	12	[	[	PUNCT
ejpam-4830	192	13	e−rseµc	e−rseµc	X
ejpam-4830	192	14	[	[	PUNCT
ejpam-4830	192	15	(	(	PUNCT
ejpam-4830	192	16	k	k	NOUN
ejpam-4830	192	17	−	−	PROPN
ejpam-4830	192	18	(	(	PUNCT
ejpam-4830	192	19	x+	x+	PROPN
ejpam-4830	192	20	ϵ)xsz	ϵ)xsz	PROPN
ejpam-4830	192	21	µc	µc	ADP
ejpam-4830	192	22	t+s	t+s	PROPN
ejpam-4830	192	23	,	,	PUNCT
ejpam-4830	192	24	t	t	NOUN
ejpam-4830	192	25	)	)	PUNCT
ejpam-4830	193	1	+	+	CCONJ
ejpam-4830	194	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	194	2	]	]	PUNCT
ejpam-4830	194	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	194	4	]	]	PUNCT
ejpam-4830	194	5	=	=	SYM
ejpam-4830	194	6	eµc	eµc	PROPN
ejpam-4830	194	7	[	[	PUNCT
ejpam-4830	194	8	(	(	PUNCT
ejpam-4830	194	9	k	k	X
ejpam-4830	194	10	−	−	PROPN
ejpam-4830	194	11	(	(	PUNCT
ejpam-4830	194	12	x+	x+	PROPN
ejpam-4830	194	13	ϵ)xsz	ϵ)xsz	PROPN
ejpam-4830	194	14	µc	µc	ADP
ejpam-4830	194	15	t+s	t+s	PROPN
ejpam-4830	194	16	,	,	PUNCT
ejpam-4830	194	17	t	t	NOUN
ejpam-4830	194	18	)	)	PUNCT
ejpam-4830	195	1	+	+	CCONJ
ejpam-4830	195	2	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	195	3	]	]	PUNCT
ejpam-4830	195	4	}	}	PUNCT
ejpam-4830	195	5	≤	≤	NUM
ejpam-4830	195	6	inf	inf	NOUN
ejpam-4830	195	7	{	{	PUNCT
ejpam-4830	195	8	s	s	PROPN
ejpam-4830	195	9	∈	∈	PROPN
ejpam-4830	196	1	[	[	X
ejpam-4830	196	2	0	0	NUM
ejpam-4830	196	3	,	,	PUNCT
ejpam-4830	196	4	t	t	PROPN
ejpam-4830	196	5	−	−	PROPN
ejpam-4830	196	6	t	t	PROPN
ejpam-4830	196	7	]	]	PUNCT
ejpam-4830	196	8	:	:	PUNCT
ejpam-4830	196	9	sup	sup	NOUN
ejpam-4830	196	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	196	11	e	e	X
ejpam-4830	196	12	[	[	PUNCT
ejpam-4830	196	13	e−rseµc	e−rseµc	X
ejpam-4830	196	14	[	[	PUNCT
ejpam-4830	196	15	(	(	PUNCT
ejpam-4830	196	16	k	k	ADJ
ejpam-4830	196	17	−	−	PROPN
ejpam-4830	196	18	xxsz	xxsz	NOUN
ejpam-4830	196	19	µc	µc	INTJ
ejpam-4830	196	20	t+s	t+s	PROPN
ejpam-4830	196	21	,	,	PUNCT
ejpam-4830	196	22	t	t	NOUN
ejpam-4830	196	23	)	)	PUNCT
ejpam-4830	197	1	+	+	CCONJ
ejpam-4830	198	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	198	2	]	]	PUNCT
ejpam-4830	198	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	198	4	]	]	PUNCT
ejpam-4830	198	5	≥	≥	X
ejpam-4830	198	6	eµc	eµc	PROPN
ejpam-4830	198	7	[	[	PUNCT
ejpam-4830	198	8	(	(	PUNCT
ejpam-4830	198	9	k	k	X
ejpam-4830	198	10	−	−	PROPN
ejpam-4830	198	11	(	(	PUNCT
ejpam-4830	198	12	x+	x+	PROPN
ejpam-4830	198	13	ϵ)xsz	ϵ)xsz	PROPN
ejpam-4830	198	14	µc	µc	ADP
ejpam-4830	198	15	t+s	t+s	PROPN
ejpam-4830	198	16	,	,	PUNCT
ejpam-4830	198	17	t	t	NOUN
ejpam-4830	198	18	)	)	PUNCT
ejpam-4830	199	1	+	+	CCONJ
ejpam-4830	199	2	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	199	3	]	]	PUNCT
ejpam-4830	199	4	}	}	PUNCT
ejpam-4830	199	5	≤	≤	NUM
ejpam-4830	199	6	inf	inf	NOUN
ejpam-4830	199	7	{	{	PUNCT
ejpam-4830	199	8	s	s	PROPN
ejpam-4830	199	9	∈	∈	PROPN
ejpam-4830	200	1	[	[	X
ejpam-4830	200	2	0	0	NUM
ejpam-4830	200	3	,	,	PUNCT
ejpam-4830	200	4	t	t	PROPN
ejpam-4830	200	5	−	−	PROPN
ejpam-4830	200	6	t	t	PROPN
ejpam-4830	200	7	]	]	PUNCT
ejpam-4830	200	8	:	:	PUNCT
ejpam-4830	200	9	sup	sup	NOUN
ejpam-4830	200	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	200	11	e	e	X
ejpam-4830	200	12	[	[	PUNCT
ejpam-4830	200	13	e−rseµc	e−rseµc	X
ejpam-4830	200	14	[	[	PUNCT
ejpam-4830	200	15	(	(	PUNCT
ejpam-4830	200	16	k	k	ADJ
ejpam-4830	200	17	−	−	PROPN
ejpam-4830	200	18	xxsz	xxsz	NOUN
ejpam-4830	200	19	µc	µc	INTJ
ejpam-4830	200	20	t+s	t+s	PROPN
ejpam-4830	200	21	,	,	PUNCT
ejpam-4830	200	22	t	t	NOUN
ejpam-4830	200	23	)	)	PUNCT
ejpam-4830	201	1	+	+	CCONJ
ejpam-4830	202	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	202	2	]	]	PUNCT
ejpam-4830	202	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	202	4	]	]	PUNCT
ejpam-4830	202	5	≥	≥	X
ejpam-4830	202	6	eµc	eµc	PROPN
ejpam-4830	202	7	[	[	PUNCT
ejpam-4830	202	8	1	1	NUM
ejpam-4830	202	9	2	2	NUM
ejpam-4830	202	10	(	(	PUNCT
ejpam-4830	202	11	k	k	NOUN
ejpam-4830	202	12	−	−	PROPN
ejpam-4830	202	13	xzµc	xzµc	PROPN
ejpam-4830	202	14	t+s	t+s	PROPN
ejpam-4830	202	15	,	,	PUNCT
ejpam-4830	202	16	t	t	PROPN
ejpam-4830	202	17	−	−	PROPN
ejpam-4830	202	18	ϵzµc	ϵzµc	PROPN
ejpam-4830	202	19	t+s	t+s	PROPN
ejpam-4830	202	20	,	,	PUNCT
ejpam-4830	202	21	t	t	PROPN
ejpam-4830	202	22	+	+	CCONJ
ejpam-4830	202	23	∣∣k	∣∣k	PROPN
ejpam-4830	202	24	−	−	PROPN
ejpam-4830	202	25	xzµc	xzµc	PROPN
ejpam-4830	202	26	t+s	t+s	PROPN
ejpam-4830	202	27	,	,	PUNCT
ejpam-4830	202	28	t	t	PROPN
ejpam-4830	202	29	−	−	PROPN
ejpam-4830	202	30	ϵzµc	ϵzµc	PROPN
ejpam-4830	202	31	t+s	t+s	PROPN
ejpam-4830	202	32	,	,	PUNCT
ejpam-4830	202	33	t	t	NOUN
ejpam-4830	202	34	∣∣	∣∣	AUX
ejpam-4830	202	35	)	)	PUNCT
ejpam-4830	202	36	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	202	37	]	]	PUNCT
ejpam-4830	202	38	}	}	PUNCT
ejpam-4830	202	39	this	this	PRON
ejpam-4830	202	40	implies	imply	VERB
ejpam-4830	202	41	that	that	SCONJ
ejpam-4830	202	42	lim	lim	PROPN
ejpam-4830	202	43	ϵ→0	ϵ→0	X
ejpam-4830	202	44	τd(t	τd(t	PROPN
ejpam-4830	202	45	,	,	PUNCT
ejpam-4830	202	46	x+	x+	PROPN
ejpam-4830	202	47	ϵ	ϵ	X
ejpam-4830	202	48	,	,	PUNCT
ejpam-4830	202	49	j	j	NOUN
ejpam-4830	202	50	)	)	PUNCT
ejpam-4830	202	51	≤	≤	PROPN
ejpam-4830	202	52	lim	lim	PROPN
ejpam-4830	202	53	ϵ→0	ϵ→0	PROPN
ejpam-4830	202	54	inf	inf	PROPN
ejpam-4830	202	55	{	{	PUNCT
ejpam-4830	202	56	s	s	PROPN
ejpam-4830	202	57	∈	∈	PROPN
ejpam-4830	203	1	[	[	X
ejpam-4830	203	2	0	0	NUM
ejpam-4830	203	3	,	,	PUNCT
ejpam-4830	203	4	t	t	PROPN
ejpam-4830	203	5	−	−	PROPN
ejpam-4830	203	6	t	t	PROPN
ejpam-4830	203	7	]	]	PUNCT
ejpam-4830	203	8	:	:	PUNCT
ejpam-4830	203	9	sup	sup	NOUN
ejpam-4830	203	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	203	11	e	e	X
ejpam-4830	203	12	[	[	PUNCT
ejpam-4830	203	13	e−rseµc	e−rseµc	X
ejpam-4830	203	14	[	[	PUNCT
ejpam-4830	203	15	(	(	PUNCT
ejpam-4830	203	16	k	k	ADJ
ejpam-4830	203	17	−	−	PROPN
ejpam-4830	203	18	xxsz	xxsz	NOUN
ejpam-4830	203	19	µc	µc	INTJ
ejpam-4830	203	20	t+s	t+s	PROPN
ejpam-4830	203	21	,	,	PUNCT
ejpam-4830	203	22	t	t	NOUN
ejpam-4830	203	23	)	)	PUNCT
ejpam-4830	204	1	+	+	CCONJ
ejpam-4830	205	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	205	2	]	]	PUNCT
ejpam-4830	205	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	205	4	]	]	PUNCT
ejpam-4830	205	5	≥	≥	X
ejpam-4830	205	6	eµc	eµc	PROPN
ejpam-4830	205	7	[	[	PUNCT
ejpam-4830	205	8	1	1	NUM
ejpam-4830	205	9	2	2	NUM
ejpam-4830	205	10	(	(	PUNCT
ejpam-4830	205	11	k	k	NOUN
ejpam-4830	205	12	−	−	PROPN
ejpam-4830	205	13	xzµc	xzµc	PROPN
ejpam-4830	205	14	t+s	t+s	PROPN
ejpam-4830	205	15	,	,	PUNCT
ejpam-4830	205	16	t	t	PROPN
ejpam-4830	205	17	−	−	PROPN
ejpam-4830	205	18	ϵzµc	ϵzµc	PROPN
ejpam-4830	205	19	t+s	t+s	PROPN
ejpam-4830	205	20	,	,	PUNCT
ejpam-4830	205	21	t	t	PROPN
ejpam-4830	205	22	+	+	CCONJ
ejpam-4830	205	23	∣∣k	∣∣k	PROPN
ejpam-4830	205	24	−	−	PROPN
ejpam-4830	205	25	xzµc	xzµc	PROPN
ejpam-4830	205	26	t+s	t+s	PROPN
ejpam-4830	205	27	,	,	PUNCT
ejpam-4830	205	28	t	t	PROPN
ejpam-4830	205	29	−	−	PROPN
ejpam-4830	205	30	ϵzµc	ϵzµc	PROPN
ejpam-4830	205	31	t+s	t+s	PROPN
ejpam-4830	205	32	,	,	PUNCT
ejpam-4830	205	33	t	t	NOUN
ejpam-4830	205	34	∣∣	∣∣	AUX
ejpam-4830	205	35	)	)	PUNCT
ejpam-4830	205	36	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	205	37	]	]	PUNCT
ejpam-4830	205	38	}	}	PUNCT
ejpam-4830	205	39	=	=	SYM
ejpam-4830	205	40	inf	inf	NOUN
ejpam-4830	205	41	{	{	PUNCT
ejpam-4830	205	42	s	s	PROPN
ejpam-4830	205	43	∈	∈	PROPN
ejpam-4830	206	1	[	[	X
ejpam-4830	206	2	0	0	NUM
ejpam-4830	206	3	,	,	PUNCT
ejpam-4830	206	4	t	t	PROPN
ejpam-4830	206	5	−	−	PROPN
ejpam-4830	206	6	t	t	PROPN
ejpam-4830	206	7	]	]	PUNCT
ejpam-4830	206	8	:	:	PUNCT
ejpam-4830	206	9	sup	sup	NOUN
ejpam-4830	206	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	206	11	e	e	X
ejpam-4830	206	12	[	[	PUNCT
ejpam-4830	206	13	e−rseµc	e−rseµc	X
ejpam-4830	206	14	[	[	PUNCT
ejpam-4830	206	15	(	(	PUNCT
ejpam-4830	206	16	k	k	ADJ
ejpam-4830	206	17	−	−	PROPN
ejpam-4830	206	18	xxsz	xxsz	NOUN
ejpam-4830	206	19	µc	µc	INTJ
ejpam-4830	206	20	t+s	t+s	PROPN
ejpam-4830	206	21	,	,	PUNCT
ejpam-4830	206	22	t	t	NOUN
ejpam-4830	206	23	)	)	PUNCT
ejpam-4830	207	1	+	+	CCONJ
ejpam-4830	208	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	208	2	]	]	PUNCT
ejpam-4830	208	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	208	4	]	]	PUNCT
ejpam-4830	208	5	≥	≥	X
ejpam-4830	208	6	eµc	eµc	PROPN
ejpam-4830	208	7	[	[	PUNCT
ejpam-4830	208	8	1	1	NUM
ejpam-4830	208	9	2	2	NUM
ejpam-4830	208	10	(	(	PUNCT
ejpam-4830	208	11	k	k	NOUN
ejpam-4830	208	12	−	−	PROPN
ejpam-4830	208	13	xzµc	xzµc	PROPN
ejpam-4830	208	14	t+s	t+s	PROPN
ejpam-4830	208	15	,	,	PUNCT
ejpam-4830	208	16	t	t	PROPN
ejpam-4830	208	17	+	+	CCONJ
ejpam-4830	208	18	∣∣k	∣∣k	PROPN
ejpam-4830	208	19	−	−	PROPN
ejpam-4830	208	20	xzµc	xzµc	PROPN
ejpam-4830	208	21	t+s	t+s	PROPN
ejpam-4830	208	22	,	,	PUNCT
ejpam-4830	208	23	t	t	NOUN
ejpam-4830	208	24	∣∣	∣∣	AUX
ejpam-4830	208	25	)	)	PUNCT
ejpam-4830	208	26	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	208	27	]	]	PUNCT
ejpam-4830	208	28	}	}	PUNCT
ejpam-4830	208	29	f.	f.	PROPN
ejpam-4830	208	30	sumalpong	sumalpong	PROPN
ejpam-4830	208	31	,	,	PUNCT
ejpam-4830	208	32	m.	m.	PROPN
ejpam-4830	208	33	frondoza	frondoza	PROPN
ejpam-4830	208	34	,	,	PUNCT
ejpam-4830	208	35	n.l	n.l	PROPN
ejpam-4830	208	36	.	.	PROPN
ejpam-4830	208	37	sayson	sayson	PROPN
ejpam-4830	208	38	/	/	SYM
ejpam-4830	208	39	eur	eur	PROPN
ejpam-4830	208	40	.	.	PUNCT
ejpam-4830	209	1	j.	j.	PROPN
ejpam-4830	209	2	pure	pure	PROPN
ejpam-4830	209	3	appl	appl	PROPN
ejpam-4830	209	4	.	.	PROPN
ejpam-4830	209	5	math	math	PROPN
ejpam-4830	209	6	,	,	PUNCT
ejpam-4830	209	7	16	16	NUM
ejpam-4830	209	8	(	(	PUNCT
ejpam-4830	209	9	3	3	NUM
ejpam-4830	209	10	)	)	PUNCT
ejpam-4830	209	11	(	(	PUNCT
ejpam-4830	209	12	2023	2023	NUM
ejpam-4830	209	13	)	)	PUNCT
ejpam-4830	209	14	,	,	PUNCT
ejpam-4830	209	15	1830	1830	NUM
ejpam-4830	209	16	-	-	SYM
ejpam-4830	209	17	1847	1847	NUM
ejpam-4830	209	18	1838	1838	NUM
ejpam-4830	209	19	=	=	SYM
ejpam-4830	209	20	inf	inf	NOUN
ejpam-4830	209	21	{	{	PUNCT
ejpam-4830	209	22	s	s	PROPN
ejpam-4830	209	23	∈	∈	PROPN
ejpam-4830	210	1	[	[	X
ejpam-4830	210	2	0	0	NUM
ejpam-4830	210	3	,	,	PUNCT
ejpam-4830	210	4	t	t	PROPN
ejpam-4830	210	5	−	−	PROPN
ejpam-4830	210	6	t	t	PROPN
ejpam-4830	210	7	]	]	PUNCT
ejpam-4830	210	8	:	:	PUNCT
ejpam-4830	210	9	sup	sup	NOUN
ejpam-4830	210	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	210	11	e	e	X
ejpam-4830	210	12	[	[	PUNCT
ejpam-4830	210	13	e−rseµc	e−rseµc	X
ejpam-4830	210	14	[	[	PUNCT
ejpam-4830	210	15	(	(	PUNCT
ejpam-4830	210	16	k	k	ADJ
ejpam-4830	210	17	−	−	PROPN
ejpam-4830	210	18	xxsz	xxsz	NOUN
ejpam-4830	210	19	µc	µc	INTJ
ejpam-4830	210	20	t+s	t+s	PROPN
ejpam-4830	210	21	,	,	PUNCT
ejpam-4830	210	22	t	t	NOUN
ejpam-4830	210	23	)	)	PUNCT
ejpam-4830	211	1	+	+	CCONJ
ejpam-4830	212	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	212	2	]	]	PUNCT
ejpam-4830	212	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	212	4	]	]	PUNCT
ejpam-4830	212	5	≥	≥	X
ejpam-4830	212	6	eµc	eµc	PROPN
ejpam-4830	212	7	[	[	PUNCT
ejpam-4830	212	8	(	(	PUNCT
ejpam-4830	212	9	k	k	ADJ
ejpam-4830	212	10	−	−	PROPN
ejpam-4830	212	11	xxsz	xxsz	NOUN
ejpam-4830	212	12	µc	µc	INTJ
ejpam-4830	212	13	t+s	t+s	PROPN
ejpam-4830	212	14	,	,	PUNCT
ejpam-4830	212	15	t	t	PROPN
ejpam-4830	212	16	)	)	PUNCT
ejpam-4830	213	1	+	+	CCONJ
ejpam-4830	213	2	]	]	X
ejpam-4830	213	3	}	}	PUNCT
ejpam-4830	213	4	=	=	SYM
ejpam-4830	213	5	inf	inf	NOUN
ejpam-4830	213	6	{	{	PUNCT
ejpam-4830	213	7	s	s	PROPN
ejpam-4830	213	8	∈	∈	PROPN
ejpam-4830	214	1	[	[	X
ejpam-4830	214	2	0	0	NUM
ejpam-4830	214	3	,	,	PUNCT
ejpam-4830	214	4	t	t	PROPN
ejpam-4830	214	5	−	−	PROPN
ejpam-4830	214	6	t	t	PROPN
ejpam-4830	214	7	]	]	PUNCT
ejpam-4830	214	8	:	:	PUNCT
ejpam-4830	214	9	sup	sup	NOUN
ejpam-4830	214	10	0≤s≤t−t	0≤s≤t−t	NUM
ejpam-4830	214	11	e	e	X
ejpam-4830	214	12	[	[	PUNCT
ejpam-4830	214	13	e−rseµc	e−rseµc	X
ejpam-4830	214	14	[	[	PUNCT
ejpam-4830	214	15	(	(	PUNCT
ejpam-4830	214	16	k	k	ADJ
ejpam-4830	214	17	−	−	PROPN
ejpam-4830	214	18	xxsz	xxsz	NOUN
ejpam-4830	214	19	µc	µc	INTJ
ejpam-4830	214	20	t+s	t+s	PROPN
ejpam-4830	214	21	,	,	PUNCT
ejpam-4830	214	22	t	t	NOUN
ejpam-4830	214	23	)	)	PUNCT
ejpam-4830	215	1	+	+	CCONJ
ejpam-4830	216	1	∣∣∣ft+s	∣∣∣ft+s	X
ejpam-4830	216	2	]	]	PUNCT
ejpam-4830	216	3	∣∣∣ft	∣∣∣ft	NOUN
ejpam-4830	216	4	]	]	PUNCT
ejpam-4830	216	5	=	=	SYM
ejpam-4830	216	6	eµc	eµc	PROPN
ejpam-4830	216	7	[	[	PUNCT
ejpam-4830	216	8	(	(	PUNCT
ejpam-4830	216	9	k	k	ADJ
ejpam-4830	216	10	−	−	PROPN
ejpam-4830	216	11	xxsz	xxsz	NOUN
ejpam-4830	216	12	µc	µc	INTJ
ejpam-4830	216	13	t+s	t+s	PROPN
ejpam-4830	216	14	,	,	PUNCT
ejpam-4830	216	15	t	t	PROPN
ejpam-4830	216	16	)	)	PUNCT
ejpam-4830	216	17	+	+	CCONJ
ejpam-4830	216	18	]	]	X
ejpam-4830	216	19	}	}	PUNCT
ejpam-4830	216	20	=	=	SYM
ejpam-4830	216	21	inf	inf	NOUN
ejpam-4830	216	22	{	{	PUNCT
ejpam-4830	216	23	s	s	NOUN
ejpam-4830	216	24	∈	∈	X
ejpam-4830	216	25	[	[	X
ejpam-4830	216	26	0	0	NUM
ejpam-4830	216	27	,	,	PUNCT
ejpam-4830	216	28	t	t	PROPN
ejpam-4830	216	29	−	−	PROPN
ejpam-4830	216	30	t	t	PROPN
ejpam-4830	216	31	]	]	PUNCT
ejpam-4830	216	32	:	:	PUNCT
ejpam-4830	216	33	(	(	PUNCT
ejpam-4830	216	34	t	t	PROPN
ejpam-4830	216	35	,	,	PUNCT
ejpam-4830	216	36	x	x	PROPN
ejpam-4830	216	37	,	,	PUNCT
ejpam-4830	216	38	j	j	NOUN
ejpam-4830	216	39	)	)	PUNCT
ejpam-4830	216	40	∈	∈	PROPN
ejpam-4830	217	1	d	d	NOUN
ejpam-4830	217	2	}	}	PUNCT
ejpam-4830	217	3	=	=	SYM
ejpam-4830	217	4	0	0	X
ejpam-4830	217	5	.	.	PUNCT
ejpam-4830	217	6	now	now	ADV
ejpam-4830	217	7	to	to	PART
ejpam-4830	217	8	prove	prove	VERB
ejpam-4830	217	9	(	(	PUNCT
ejpam-4830	217	10	26	26	NUM
ejpam-4830	217	11	)	)	PUNCT
ejpam-4830	217	12	,	,	PUNCT
ejpam-4830	217	13	we	we	PRON
ejpam-4830	217	14	use	use	VERB
ejpam-4830	217	15	(	(	PUNCT
ejpam-4830	217	16	28	28	NUM
ejpam-4830	217	17	)	)	PUNCT
ejpam-4830	217	18	.	.	PUNCT
ejpam-4830	218	1	thus	thus	ADV
ejpam-4830	218	2	,	,	PUNCT
ejpam-4830	218	3	we	we	PRON
ejpam-4830	218	4	have	have	VERB
ejpam-4830	218	5	lim	lim	PROPN
ejpam-4830	218	6	sup	sup	PROPN
ejpam-4830	218	7	ϵ	ϵ	PROPN
ejpam-4830	218	8	↘	↘	PROPN
ejpam-4830	218	9	0	0	PROPN
ejpam-4830	218	10	v	v	PROPN
ejpam-4830	218	11	(	(	PUNCT
ejpam-4830	218	12	t	t	PROPN
ejpam-4830	218	13	,	,	PUNCT
ejpam-4830	218	14	x+	x+	PROPN
ejpam-4830	219	1	ϵ	ϵ	X
ejpam-4830	219	2	,	,	PUNCT
ejpam-4830	219	3	j)−	j)−	PROPN
ejpam-4830	219	4	v	v	PROPN
ejpam-4830	219	5	(	(	PUNCT
ejpam-4830	219	6	t	t	PROPN
ejpam-4830	219	7	,	,	PUNCT
ejpam-4830	219	8	x	x	NOUN
ejpam-4830	219	9	,	,	PUNCT
ejpam-4830	219	10	j	j	PROPN
ejpam-4830	219	11	)	)	PUNCT
ejpam-4830	219	12	ϵ	ϵ	X
ejpam-4830	220	1	=	=	SYM
ejpam-4830	220	2	lim	lim	PROPN
ejpam-4830	220	3	sup	sup	PROPN
ejpam-4830	220	4	ϵ	ϵ	X
ejpam-4830	220	5	↘	↘	PROPN
ejpam-4830	220	6	0	0	NUM
ejpam-4830	220	7	1	1	NUM
ejpam-4830	220	8	ϵ	ϵ	NOUN
ejpam-4830	220	9	{	{	PUNCT
ejpam-4830	220	10	e	e	X
ejpam-4830	220	11	[	[	PUNCT
ejpam-4830	220	12	e−rτ+ϵ	e−rτ+ϵ	NUM
ejpam-4830	220	13	gµc	gµc	NOUN
ejpam-4830	220	14	(	(	PUNCT
ejpam-4830	220	15	t+	t+	NOUN
ejpam-4830	220	16	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	220	17	,	,	PUNCT
ejpam-4830	220	18	x+	x+	PROPN
ejpam-4830	220	19	ϵ	ϵ	X
ejpam-4830	220	20	,	,	PUNCT
ejpam-4830	220	21	j	j	PROPN
ejpam-4830	220	22	)	)	PUNCT
ejpam-4830	220	23	∣∣∣ft	∣∣∣ft	PUNCT
ejpam-4830	220	24	]	]	PUNCT
ejpam-4830	221	1	−	−	NUM
ejpam-4830	221	2	sup	sup	NOUN
ejpam-4830	221	3	0≤τ≤t−t	0≤τ≤t−t	PROPN
ejpam-4830	221	4	e	e	NOUN
ejpam-4830	221	5	[	[	PUNCT
ejpam-4830	221	6	e−rτ+ϵ	e−rτ+ϵ	NUM
ejpam-4830	221	7	gµc	gµc	NOUN
ejpam-4830	221	8	(	(	PUNCT
ejpam-4830	221	9	t+	t+	NOUN
ejpam-4830	221	10	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	221	11	,	,	PUNCT
ejpam-4830	221	12	x	x	PROPN
ejpam-4830	221	13	,	,	PUNCT
ejpam-4830	221	14	j	j	NOUN
ejpam-4830	221	15	)	)	PUNCT
ejpam-4830	221	16	)	)	PUNCT
ejpam-4830	222	1	∣∣∣ft	∣∣∣ft	PUNCT
ejpam-4830	222	2	]	]	PUNCT
ejpam-4830	222	3	}	}	PUNCT
ejpam-4830	222	4	≤	≤	NUM
ejpam-4830	222	5	lim	lim	PROPN
ejpam-4830	222	6	sup	sup	PROPN
ejpam-4830	222	7	ϵ	ϵ	PROPN
ejpam-4830	222	8	↘	↘	PROPN
ejpam-4830	222	9	0	0	NUM
ejpam-4830	222	10	1	1	NUM
ejpam-4830	222	11	ϵ	ϵ	NOUN
ejpam-4830	222	12	{	{	PUNCT
ejpam-4830	222	13	e	e	X
ejpam-4830	222	14	[	[	PUNCT
ejpam-4830	222	15	e−rτ+ϵ	e−rτ+ϵ	NUM
ejpam-4830	222	16	gµc	gµc	NOUN
ejpam-4830	222	17	(	(	PUNCT
ejpam-4830	222	18	t+	t+	NOUN
ejpam-4830	222	19	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	222	20	,	,	PUNCT
ejpam-4830	222	21	x+	x+	PROPN
ejpam-4830	222	22	ϵ	ϵ	X
ejpam-4830	222	23	,	,	PUNCT
ejpam-4830	222	24	j	j	PROPN
ejpam-4830	222	25	)	)	PUNCT
ejpam-4830	222	26	∣∣∣ft	∣∣∣ft	PUNCT
ejpam-4830	222	27	]	]	PUNCT
ejpam-4830	222	28	−	−	PUNCT
ejpam-4830	222	29	e	e	X
ejpam-4830	222	30	[	[	PUNCT
ejpam-4830	222	31	e−rτ+ϵ	e−rτ+ϵ	NUM
ejpam-4830	222	32	gµc	gµc	NOUN
ejpam-4830	222	33	(	(	PUNCT
ejpam-4830	222	34	t+	t+	NOUN
ejpam-4830	222	35	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	222	36	,	,	PUNCT
ejpam-4830	222	37	x	x	PROPN
ejpam-4830	222	38	,	,	PUNCT
ejpam-4830	222	39	j	j	NOUN
ejpam-4830	222	40	)	)	PUNCT
ejpam-4830	222	41	)	)	PUNCT
ejpam-4830	222	42	∣∣∣ft	∣∣∣ft	PUNCT
ejpam-4830	222	43	]	]	PUNCT
ejpam-4830	222	44	}	}	PUNCT
ejpam-4830	222	45	≤	≤	NUM
ejpam-4830	222	46	lim	lim	PROPN
ejpam-4830	222	47	sup	sup	PROPN
ejpam-4830	222	48	ϵ	ϵ	PROPN
ejpam-4830	222	49	↘	↘	PROPN
ejpam-4830	222	50	0	0	NUM
ejpam-4830	222	51	1	1	NUM
ejpam-4830	222	52	ϵ	ϵ	NOUN
ejpam-4830	222	53	{	{	PUNCT
ejpam-4830	222	54	gµc	gµc	NOUN
ejpam-4830	222	55	(	(	PUNCT
ejpam-4830	222	56	t+	t+	NOUN
ejpam-4830	222	57	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	222	58	,	,	PUNCT
ejpam-4830	222	59	x+	x+	PROPN
ejpam-4830	222	60	ϵ	ϵ	X
ejpam-4830	222	61	,	,	PUNCT
ejpam-4830	222	62	j	j	PROPN
ejpam-4830	222	63	)	)	PUNCT
ejpam-4830	222	64	−gµc	−gµc	NOUN
ejpam-4830	222	65	(	(	PUNCT
ejpam-4830	222	66	t+	t+	X
ejpam-4830	222	67	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	222	68	,	,	PUNCT
ejpam-4830	222	69	x	x	PROPN
ejpam-4830	222	70	,	,	PUNCT
ejpam-4830	222	71	j	j	PROPN
ejpam-4830	222	72	)	)	PUNCT
ejpam-4830	222	73	)	)	PUNCT
ejpam-4830	222	74	}	}	PUNCT
ejpam-4830	223	1	=	=	SYM
ejpam-4830	223	2	∂gµc	∂gµc	NOUN
ejpam-4830	223	3	∂x	∂x	PROPN
ejpam-4830	223	4	(	(	PUNCT
ejpam-4830	223	5	t	t	PROPN
ejpam-4830	223	6	,	,	PUNCT
ejpam-4830	223	7	x	x	PROPN
ejpam-4830	223	8	,	,	PUNCT
ejpam-4830	223	9	j	j	PROPN
ejpam-4830	223	10	)	)	PUNCT
ejpam-4830	223	11	,	,	PUNCT
ejpam-4830	223	12	(	(	PUNCT
ejpam-4830	223	13	30	30	NUM
ejpam-4830	223	14	)	)	PUNCT
ejpam-4830	223	15	hence	hence	ADV
ejpam-4830	223	16	we	we	PRON
ejpam-4830	223	17	conclude	conclude	VERB
ejpam-4830	223	18	(	(	PUNCT
ejpam-4830	223	19	26	26	NUM
ejpam-4830	223	20	)	)	PUNCT
ejpam-4830	223	21	.	.	PUNCT
ejpam-4830	224	1	it	it	PRON
ejpam-4830	224	2	is	be	AUX
ejpam-4830	224	3	well	well	ADV
ejpam-4830	224	4	-	-	PUNCT
ejpam-4830	224	5	known	know	VERB
ejpam-4830	224	6	that	that	SCONJ
ejpam-4830	224	7	every	every	DET
ejpam-4830	224	8	convex	convex	NOUN
ejpam-4830	224	9	functions	function	NOUN
ejpam-4830	224	10	on	on	ADP
ejpam-4830	224	11	the	the	DET
ejpam-4830	224	12	open	open	ADJ
ejpam-4830	224	13	interval	interval	NOUN
ejpam-4830	224	14	i	i	PRON
ejpam-4830	224	15	are	be	AUX
ejpam-4830	224	16	differentiable	differentiable	ADJ
ejpam-4830	224	17	almost	almost	ADV
ejpam-4830	224	18	everywhere	everywhere	ADV
ejpam-4830	224	19	,	,	PUNCT
ejpam-4830	224	20	e.g.	e.g.	ADV
ejpam-4830	224	21	[	[	X
ejpam-4830	224	22	3	3	NUM
ejpam-4830	224	23	]	]	PUNCT
ejpam-4830	224	24	.	.	PUNCT
ejpam-4830	225	1	in	in	ADP
ejpam-4830	225	2	the	the	DET
ejpam-4830	225	3	following	follow	VERB
ejpam-4830	225	4	lemmas	lemmas	PROPN
ejpam-4830	225	5	,	,	PUNCT
ejpam-4830	225	6	we	we	PRON
ejpam-4830	225	7	use	use	VERB
ejpam-4830	225	8	the	the	DET
ejpam-4830	225	9	fact	fact	NOUN
ejpam-4830	225	10	that	that	SCONJ
ejpam-4830	225	11	both	both	PRON
ejpam-4830	225	12	v	v	NOUN
ejpam-4830	225	13	(	(	PUNCT
ejpam-4830	225	14	t	t	PROPN
ejpam-4830	225	15	,	,	PUNCT
ejpam-4830	225	16	x	x	NOUN
ejpam-4830	225	17	,	,	PUNCT
ejpam-4830	225	18	j	j	PROPN
ejpam-4830	225	19	)	)	PUNCT
ejpam-4830	225	20	and	and	CCONJ
ejpam-4830	225	21	gµc(t	gµc(t	NOUN
ejpam-4830	225	22	,	,	PUNCT
ejpam-4830	225	23	x	x	NOUN
ejpam-4830	225	24	,	,	PUNCT
ejpam-4830	225	25	j	j	NOUN
ejpam-4830	225	26	)	)	PUNCT
ejpam-4830	225	27	are	be	AUX
ejpam-4830	225	28	differentiable	differentiable	ADJ
ejpam-4830	225	29	p	p	NOUN
ejpam-4830	225	30	-	-	PUNCT
ejpam-4830	225	31	almost	almost	ADV
ejpam-4830	225	32	surely	surely	ADV
ejpam-4830	225	33	for	for	ADP
ejpam-4830	225	34	all	all	PRON
ejpam-4830	225	35	x	x	SYM
ejpam-4830	225	36	on	on	ADP
ejpam-4830	225	37	(	(	PUNCT
ejpam-4830	225	38	0,∞	0,∞	NUM
ejpam-4830	225	39	)	)	PUNCT
ejpam-4830	225	40	.	.	PUNCT
ejpam-4830	226	1	lemma	lemma	PROPN
ejpam-4830	226	2	4	4	X
ejpam-4830	226	3	.	.	PUNCT
ejpam-4830	227	1	the	the	DET
ejpam-4830	227	2	functions	function	NOUN
ejpam-4830	227	3	∂v	∂v	PROPN
ejpam-4830	227	4	∂x	∂x	PROPN
ejpam-4830	227	5	(	(	PUNCT
ejpam-4830	227	6	t	t	PROPN
ejpam-4830	227	7	,	,	PUNCT
ejpam-4830	227	8	x	x	PROPN
ejpam-4830	227	9	,	,	PUNCT
ejpam-4830	227	10	j	j	PROPN
ejpam-4830	227	11	)	)	PUNCT
ejpam-4830	227	12	and	and	CCONJ
ejpam-4830	227	13	∂gµc	∂gµc	PRON
ejpam-4830	227	14	∂x	∂x	PROPN
ejpam-4830	227	15	(	(	PUNCT
ejpam-4830	227	16	t	t	PROPN
ejpam-4830	227	17	,	,	PUNCT
ejpam-4830	227	18	x	x	PROPN
ejpam-4830	227	19	,	,	PUNCT
ejpam-4830	227	20	j	j	NOUN
ejpam-4830	227	21	)	)	PUNCT
ejpam-4830	227	22	are	be	AUX
ejpam-4830	227	23	continuous	continuous	ADJ
ejpam-4830	227	24	on	on	ADP
ejpam-4830	227	25	(	(	PUNCT
ejpam-4830	227	26	0,∞	0,∞	NOUN
ejpam-4830	227	27	)	)	PUNCT
ejpam-4830	227	28	p	p	NOUN
ejpam-4830	227	29	-	-	PUNCT
ejpam-4830	227	30	almost	almost	ADV
ejpam-4830	227	31	surely	surely	ADV
ejpam-4830	227	32	for	for	ADP
ejpam-4830	227	33	fixed	fix	VERB
ejpam-4830	227	34	t	t	PROPN
ejpam-4830	227	35	∈	∈	PROPN
ejpam-4830	228	1	[	[	X
ejpam-4830	228	2	0	0	NUM
ejpam-4830	228	3	,	,	PUNCT
ejpam-4830	228	4	t	t	NOUN
ejpam-4830	228	5	]	]	PUNCT
ejpam-4830	228	6	and	and	CCONJ
ejpam-4830	228	7	j	j	PROPN
ejpam-4830	228	8	∈	∈	PROPN
ejpam-4830	228	9	m.	m.	NOUN
ejpam-4830	228	10	proof	proof	NOUN
ejpam-4830	228	11	.	.	PUNCT
ejpam-4830	229	1	let	let	VERB
ejpam-4830	229	2	ϵ	ϵ	NOUN
ejpam-4830	229	3	and	and	CCONJ
ejpam-4830	229	4	c	c	PROPN
ejpam-4830	229	5	∈	∈	PROPN
ejpam-4830	229	6	(	(	PUNCT
ejpam-4830	229	7	0,∞	0,∞	NOUN
ejpam-4830	229	8	)	)	PUNCT
ejpam-4830	229	9	be	be	AUX
ejpam-4830	229	10	arbitrary	arbitrary	ADJ
ejpam-4830	229	11	.	.	PUNCT
ejpam-4830	230	1	since	since	SCONJ
ejpam-4830	230	2	v	v	NUM
ejpam-4830	230	3	(	(	PUNCT
ejpam-4830	230	4	t	t	PROPN
ejpam-4830	230	5	,	,	PUNCT
ejpam-4830	230	6	x	x	PROPN
ejpam-4830	230	7	,	,	PUNCT
ejpam-4830	230	8	j	j	NOUN
ejpam-4830	230	9	)	)	PUNCT
ejpam-4830	230	10	is	be	AUX
ejpam-4830	230	11	differentiable	differentiable	ADJ
ejpam-4830	230	12	for	for	ADP
ejpam-4830	230	13	all	all	DET
ejpam-4830	230	14	x	x	SYM
ejpam-4830	230	15	∈	∈	PROPN
ejpam-4830	230	16	(	(	PUNCT
ejpam-4830	230	17	0,∞	0,∞	NOUN
ejpam-4830	230	18	)	)	PUNCT
ejpam-4830	230	19	for	for	ADP
ejpam-4830	230	20	fixed	fix	VERB
ejpam-4830	230	21	t	t	PROPN
ejpam-4830	230	22	∈	∈	PROPN
ejpam-4830	231	1	[	[	X
ejpam-4830	231	2	0	0	NUM
ejpam-4830	231	3	,	,	PUNCT
ejpam-4830	231	4	t	t	NOUN
ejpam-4830	231	5	]	]	PUNCT
ejpam-4830	231	6	and	and	CCONJ
ejpam-4830	231	7	j	j	PROPN
ejpam-4830	231	8	∈	∈	PROPN
ejpam-4830	231	9	m	m	PROPN
ejpam-4830	231	10	,	,	PUNCT
ejpam-4830	231	11	we	we	PRON
ejpam-4830	231	12	know	know	VERB
ejpam-4830	231	13	that	that	SCONJ
ejpam-4830	231	14	there	there	PRON
ejpam-4830	231	15	exists	exist	VERB
ejpam-4830	231	16	δ	δ	PROPN
ejpam-4830	231	17	>	>	X
ejpam-4830	231	18	0	0	NUM
ejpam-4830	232	1	such	such	ADJ
ejpam-4830	232	2	that∣∣∣∣∣v	that∣∣∣∣∣v	NOUN
ejpam-4830	232	3	(	(	PUNCT
ejpam-4830	232	4	t	t	PROPN
ejpam-4830	232	5	,	,	PUNCT
ejpam-4830	232	6	x	x	X
ejpam-4830	232	7	,	,	PUNCT
ejpam-4830	232	8	j)−	j)−	PROPN
ejpam-4830	232	9	v	v	PROPN
ejpam-4830	232	10	(	(	PUNCT
ejpam-4830	232	11	t	t	PROPN
ejpam-4830	232	12	,	,	PUNCT
ejpam-4830	232	13	c	c	X
ejpam-4830	232	14	,	,	PUNCT
ejpam-4830	232	15	j	j	NOUN
ejpam-4830	232	16	)	)	PUNCT
ejpam-4830	232	17	c−	c−	NOUN
ejpam-4830	232	18	x	x	X
ejpam-4830	232	19	−	−	PROPN
ejpam-4830	232	20	∂v	∂v	PROPN
ejpam-4830	232	21	∂x	∂x	PROPN
ejpam-4830	232	22	(	(	PUNCT
ejpam-4830	232	23	t	t	PROPN
ejpam-4830	232	24	,	,	PUNCT
ejpam-4830	232	25	c	c	X
ejpam-4830	232	26	,	,	PUNCT
ejpam-4830	232	27	j	j	PROPN
ejpam-4830	232	28	)	)	PUNCT
ejpam-4830	232	29	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	232	30	<	<	X
ejpam-4830	232	31	ϵ	ϵ	X
ejpam-4830	232	32	2	2	NUM
ejpam-4830	232	33	(	(	PUNCT
ejpam-4830	232	34	31	31	NUM
ejpam-4830	232	35	)	)	PUNCT
ejpam-4830	232	36	whenever	whenever	SCONJ
ejpam-4830	232	37	0	0	NUM
ejpam-4830	232	38	<	<	X
ejpam-4830	232	39	|c	|c	VERB
ejpam-4830	232	40	−	−	PROPN
ejpam-4830	232	41	x|	x|	X
ejpam-4830	232	42	<	<	X
ejpam-4830	232	43	δ/2	δ/2	NUM
ejpam-4830	232	44	.	.	PUNCT
ejpam-4830	233	1	moreover	moreover	ADV
ejpam-4830	233	2	,	,	PUNCT
ejpam-4830	233	3	by	by	ADP
ejpam-4830	233	4	mean	mean	ADJ
ejpam-4830	233	5	-	-	PUNCT
ejpam-4830	233	6	value	value	NOUN
ejpam-4830	233	7	theorem	theorem	NOUN
ejpam-4830	233	8	,	,	PUNCT
ejpam-4830	233	9	there	there	PRON
ejpam-4830	233	10	is	be	VERB
ejpam-4830	233	11	an	an	DET
ejpam-4830	233	12	element	element	NOUN
ejpam-4830	233	13	f.	f.	PROPN
ejpam-4830	233	14	sumalpong	sumalpong	PROPN
ejpam-4830	233	15	,	,	PUNCT
ejpam-4830	233	16	m.	m.	PROPN
ejpam-4830	233	17	frondoza	frondoza	PROPN
ejpam-4830	233	18	,	,	PUNCT
ejpam-4830	233	19	n.l	n.l	PROPN
ejpam-4830	233	20	.	.	PROPN
ejpam-4830	233	21	sayson	sayson	PROPN
ejpam-4830	233	22	/	/	SYM
ejpam-4830	233	23	eur	eur	PROPN
ejpam-4830	233	24	.	.	PUNCT
ejpam-4830	234	1	j.	j.	PROPN
ejpam-4830	234	2	pure	pure	PROPN
ejpam-4830	234	3	appl	appl	PROPN
ejpam-4830	234	4	.	.	PROPN
ejpam-4830	234	5	math	math	PROPN
ejpam-4830	234	6	,	,	PUNCT
ejpam-4830	234	7	16	16	NUM
ejpam-4830	234	8	(	(	PUNCT
ejpam-4830	234	9	3	3	NUM
ejpam-4830	234	10	)	)	PUNCT
ejpam-4830	234	11	(	(	PUNCT
ejpam-4830	234	12	2023	2023	NUM
ejpam-4830	234	13	)	)	PUNCT
ejpam-4830	234	14	,	,	PUNCT
ejpam-4830	234	15	1830	1830	NUM
ejpam-4830	234	16	-	-	SYM
ejpam-4830	234	17	1847	1847	NUM
ejpam-4830	234	18	1839	1839	NUM
ejpam-4830	234	19	y	y	PROPN
ejpam-4830	234	20	∈	∈	PROPN
ejpam-4830	234	21	(	(	PUNCT
ejpam-4830	234	22	x	x	X
ejpam-4830	234	23	,	,	PUNCT
ejpam-4830	234	24	c	c	NOUN
ejpam-4830	234	25	)	)	PUNCT
ejpam-4830	234	26	such	such	ADJ
ejpam-4830	234	27	that	that	PRON
ejpam-4830	234	28	v	v	NOUN
ejpam-4830	234	29	(	(	PUNCT
ejpam-4830	234	30	t	t	PROPN
ejpam-4830	234	31	,	,	PUNCT
ejpam-4830	234	32	x	x	X
ejpam-4830	234	33	,	,	PUNCT
ejpam-4830	234	34	j)−	j)−	PROPN
ejpam-4830	234	35	v	v	PROPN
ejpam-4830	234	36	(	(	PUNCT
ejpam-4830	234	37	t	t	PROPN
ejpam-4830	234	38	,	,	PUNCT
ejpam-4830	234	39	c	c	X
ejpam-4830	234	40	,	,	PUNCT
ejpam-4830	234	41	j	j	NOUN
ejpam-4830	234	42	)	)	PUNCT
ejpam-4830	234	43	c−	c−	NOUN
ejpam-4830	234	44	x	x	X
ejpam-4830	234	45	=	=	SYM
ejpam-4830	234	46	∂v	∂v	PROPN
ejpam-4830	234	47	∂x	∂x	PROPN
ejpam-4830	234	48	(	(	PUNCT
ejpam-4830	234	49	t	t	PROPN
ejpam-4830	234	50	,	,	PUNCT
ejpam-4830	234	51	y	y	PROPN
ejpam-4830	234	52	,	,	PUNCT
ejpam-4830	234	53	j	j	PROPN
ejpam-4830	234	54	)	)	PUNCT
ejpam-4830	234	55	and	and	CCONJ
ejpam-4830	234	56	inequality	inequality	NOUN
ejpam-4830	234	57	(	(	PUNCT
ejpam-4830	234	58	31	31	NUM
ejpam-4830	234	59	)	)	PUNCT
ejpam-4830	234	60	becomes∣∣∣∣∣∂v∂x	becomes∣∣∣∣∣∂v∂x	PROPN
ejpam-4830	234	61	(	(	PUNCT
ejpam-4830	234	62	t	t	PROPN
ejpam-4830	234	63	,	,	PUNCT
ejpam-4830	234	64	y	y	PROPN
ejpam-4830	234	65	,	,	PUNCT
ejpam-4830	234	66	j)−	j)−	PROPN
ejpam-4830	234	67	∂v	∂v	PROPN
ejpam-4830	234	68	∂x	∂x	PROPN
ejpam-4830	234	69	(	(	PUNCT
ejpam-4830	234	70	t	t	PROPN
ejpam-4830	234	71	,	,	PUNCT
ejpam-4830	234	72	c	c	X
ejpam-4830	234	73	,	,	PUNCT
ejpam-4830	234	74	j	j	PROPN
ejpam-4830	234	75	)	)	PUNCT
ejpam-4830	235	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	235	2	<	<	X
ejpam-4830	235	3	ϵ	ϵ	X
ejpam-4830	235	4	2	2	NUM
ejpam-4830	235	5	.	.	PUNCT
ejpam-4830	236	1	(	(	PUNCT
ejpam-4830	236	2	32	32	NUM
ejpam-4830	236	3	)	)	PUNCT
ejpam-4830	236	4	note	note	NOUN
ejpam-4830	236	5	that	that	SCONJ
ejpam-4830	236	6	we	we	PRON
ejpam-4830	236	7	have	have	VERB
ejpam-4830	236	8	0	0	NUM
ejpam-4830	236	9	<	<	X
ejpam-4830	236	10	|y	|y	NOUN
ejpam-4830	236	11	−	−	PROPN
ejpam-4830	236	12	c|	c|	PROPN
ejpam-4830	236	13	<	<	X
ejpam-4830	236	14	|x−	|x−	PROPN
ejpam-4830	236	15	c|	c|	PROPN
ejpam-4830	236	16	<	<	X
ejpam-4830	236	17	δ/2	δ/2	NUM
ejpam-4830	236	18	.	.	PUNCT
ejpam-4830	237	1	for	for	ADP
ejpam-4830	237	2	t	t	PROPN
ejpam-4830	237	3	∈	∈	PROPN
ejpam-4830	238	1	[	[	X
ejpam-4830	238	2	0	0	NUM
ejpam-4830	238	3	,	,	PUNCT
ejpam-4830	238	4	t	t	NOUN
ejpam-4830	238	5	]	]	PUNCT
ejpam-4830	238	6	and	and	CCONJ
ejpam-4830	238	7	j	j	PROPN
ejpam-4830	238	8	∈	∈	PROPN
ejpam-4830	238	9	m	m	AUX
ejpam-4830	238	10	given	give	VERB
ejpam-4830	238	11	and	and	CCONJ
ejpam-4830	238	12	fixed	fix	VERB
ejpam-4830	238	13	,	,	PUNCT
ejpam-4830	238	14	we	we	PRON
ejpam-4830	238	15	know	know	VERB
ejpam-4830	238	16	from	from	ADP
ejpam-4830	238	17	proposition	proposition	NOUN
ejpam-4830	238	18	1	1	NUM
ejpam-4830	238	19	that	that	PRON
ejpam-4830	238	20	v	v	X
ejpam-4830	238	21	(	(	PUNCT
ejpam-4830	238	22	t	t	PROPN
ejpam-4830	238	23	,	,	PUNCT
ejpam-4830	238	24	x	x	PROPN
ejpam-4830	238	25	,	,	PUNCT
ejpam-4830	238	26	j	j	NOUN
ejpam-4830	238	27	)	)	PUNCT
ejpam-4830	238	28	is	be	AUX
ejpam-4830	238	29	convex	convex	ADJ
ejpam-4830	238	30	for	for	ADP
ejpam-4830	238	31	all	all	DET
ejpam-4830	238	32	x	x	SYM
ejpam-4830	238	33	∈	∈	PROPN
ejpam-4830	238	34	(	(	PUNCT
ejpam-4830	238	35	0,∞	0,∞	NOUN
ejpam-4830	238	36	)	)	PUNCT
ejpam-4830	238	37	,	,	PUNCT
ejpam-4830	238	38	then	then	ADV
ejpam-4830	238	39	∂v	∂v	PROPN
ejpam-4830	238	40	∂x	∂x	PROPN
ejpam-4830	238	41	(	(	PUNCT
ejpam-4830	238	42	t	t	PROPN
ejpam-4830	238	43	,	,	PUNCT
ejpam-4830	238	44	x	x	PROPN
ejpam-4830	238	45	,	,	PUNCT
ejpam-4830	238	46	j	j	NOUN
ejpam-4830	238	47	)	)	PUNCT
ejpam-4830	238	48	is	be	AUX
ejpam-4830	238	49	monotonically	monotonically	ADV
ejpam-4830	238	50	increasing	increase	VERB
ejpam-4830	238	51	.	.	PUNCT
ejpam-4830	239	1	thus	thus	ADV
ejpam-4830	239	2	,	,	PUNCT
ejpam-4830	239	3	if	if	SCONJ
ejpam-4830	239	4	0	0	NUM
ejpam-4830	239	5	<	<	X
ejpam-4830	239	6	|x−	|x−	X
ejpam-4830	239	7	y|	y|	NOUN
ejpam-4830	239	8	<	<	X
ejpam-4830	239	9	δ/2	δ/2	NUM
ejpam-4830	239	10	we	we	PRON
ejpam-4830	239	11	have∣∣∣∣∣∂v∂x	have∣∣∣∣∣∂v∂x	PROPN
ejpam-4830	239	12	(	(	PUNCT
ejpam-4830	239	13	t	t	PROPN
ejpam-4830	239	14	,	,	PUNCT
ejpam-4830	239	15	x	x	X
ejpam-4830	239	16	,	,	PUNCT
ejpam-4830	239	17	j)−	j)−	PROPN
ejpam-4830	239	18	∂v	∂v	PROPN
ejpam-4830	239	19	∂x	∂x	PROPN
ejpam-4830	239	20	(	(	PUNCT
ejpam-4830	239	21	t	t	PROPN
ejpam-4830	239	22	,	,	PUNCT
ejpam-4830	239	23	y	y	PROPN
ejpam-4830	239	24	,	,	PUNCT
ejpam-4830	239	25	j	j	PROPN
ejpam-4830	239	26	)	)	PUNCT
ejpam-4830	240	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	240	2	<	<	X
ejpam-4830	240	3	ϵ	ϵ	X
ejpam-4830	240	4	2	2	NUM
ejpam-4830	240	5	.	.	PUNCT
ejpam-4830	241	1	(	(	PUNCT
ejpam-4830	241	2	33	33	NUM
ejpam-4830	241	3	)	)	PUNCT
ejpam-4830	241	4	therefore	therefore	ADV
ejpam-4830	241	5	,	,	PUNCT
ejpam-4830	241	6	combining	combine	VERB
ejpam-4830	241	7	inequalities	inequality	NOUN
ejpam-4830	241	8	(	(	PUNCT
ejpam-4830	241	9	32	32	NUM
ejpam-4830	241	10	)	)	PUNCT
ejpam-4830	241	11	and	and	CCONJ
ejpam-4830	241	12	(	(	PUNCT
ejpam-4830	241	13	33	33	NUM
ejpam-4830	241	14	)	)	PUNCT
ejpam-4830	241	15	we	we	PRON
ejpam-4830	241	16	have∣∣∣∣∣∂v∂x	have∣∣∣∣∣∂v∂x	PROPN
ejpam-4830	241	17	(	(	PUNCT
ejpam-4830	241	18	t	t	PROPN
ejpam-4830	241	19	,	,	PUNCT
ejpam-4830	241	20	x	x	X
ejpam-4830	241	21	,	,	PUNCT
ejpam-4830	241	22	j)−	j)−	PROPN
ejpam-4830	241	23	∂v	∂v	PROPN
ejpam-4830	241	24	∂x	∂x	PROPN
ejpam-4830	241	25	(	(	PUNCT
ejpam-4830	241	26	t	t	PROPN
ejpam-4830	241	27	,	,	PUNCT
ejpam-4830	241	28	c	c	X
ejpam-4830	241	29	,	,	PUNCT
ejpam-4830	241	30	j	j	PROPN
ejpam-4830	241	31	)	)	PUNCT
ejpam-4830	242	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4830	242	2	<	<	X
ejpam-4830	243	1	ϵ	ϵ	X
ejpam-4830	243	2	,	,	PUNCT
ejpam-4830	243	3	whenever	whenever	SCONJ
ejpam-4830	243	4	0	0	NUM
ejpam-4830	243	5	<	<	X
ejpam-4830	243	6	|x−	|x−	PROPN
ejpam-4830	243	7	c|	c|	PROPN
ejpam-4830	243	8	≤	≤	PROPN
ejpam-4830	243	9	|x−	|x−	PROPN
ejpam-4830	243	10	y|+	y|+	PROPN
ejpam-4830	243	11	|y	|y	NOUN
ejpam-4830	243	12	−	−	PROPN
ejpam-4830	243	13	c|	c|	PROPN
ejpam-4830	243	14	<	<	X
ejpam-4830	243	15	δ	δ	PROPN
ejpam-4830	243	16	.	.	PUNCT
ejpam-4830	244	1	furthermore	furthermore	ADV
ejpam-4830	244	2	,	,	PUNCT
ejpam-4830	244	3	by	by	ADP
ejpam-4830	244	4	lemma	lemma	PROPN
ejpam-4830	244	5	6	6	NUM
ejpam-4830	244	6	and	and	CCONJ
ejpam-4830	244	7	the	the	DET
ejpam-4830	244	8	fact	fact	NOUN
ejpam-4830	244	9	that	that	SCONJ
ejpam-4830	244	10	∂gµc	∂gµc	NOUN
ejpam-4830	244	11	∂x	∂x	PROPN
ejpam-4830	244	12	is	be	AUX
ejpam-4830	244	13	monotonically	monotonically	ADV
ejpam-4830	244	14	increasing	increase	VERB
ejpam-4830	244	15	and	and	CCONJ
ejpam-4830	244	16	that	that	DET
ejpam-4830	244	17	v	v	NOUN
ejpam-4830	244	18	=	=	NOUN
ejpam-4830	244	19	gµc	gµc	NOUN
ejpam-4830	244	20	in	in	ADP
ejpam-4830	244	21	the	the	DET
ejpam-4830	244	22	stopping	stopping	NOUN
ejpam-4830	244	23	set	set	VERB
ejpam-4830	244	24	d	d	NOUN
ejpam-4830	244	25	which	which	PRON
ejpam-4830	244	26	is	be	AUX
ejpam-4830	244	27	defined	define	VERB
ejpam-4830	244	28	in	in	ADP
ejpam-4830	244	29	(	(	PUNCT
ejpam-4830	244	30	24	24	NUM
ejpam-4830	244	31	)	)	PUNCT
ejpam-4830	244	32	above	above	ADV
ejpam-4830	244	33	,	,	PUNCT
ejpam-4830	244	34	we	we	PRON
ejpam-4830	244	35	have	have	VERB
ejpam-4830	244	36	v	v	NUM
ejpam-4830	244	37	(	(	PUNCT
ejpam-4830	244	38	t	t	PROPN
ejpam-4830	244	39	,	,	PUNCT
ejpam-4830	244	40	x2	x2	PROPN
ejpam-4830	244	41	,	,	PUNCT
ejpam-4830	244	42	j)−	j)−	PROPN
ejpam-4830	244	43	v	v	PROPN
ejpam-4830	244	44	(	(	PUNCT
ejpam-4830	244	45	t	t	PROPN
ejpam-4830	244	46	,	,	PUNCT
ejpam-4830	244	47	x1	x1	PROPN
ejpam-4830	244	48	,	,	PUNCT
ejpam-4830	244	49	j	j	PROPN
ejpam-4830	244	50	)	)	PUNCT
ejpam-4830	245	1	x2	x2	NOUN
ejpam-4830	245	2	−	−	PROPN
ejpam-4830	246	1	x1	x1	PROPN
ejpam-4830	246	2	=	=	PUNCT
ejpam-4830	246	3	∂v	∂v	PROPN
ejpam-4830	246	4	∂x	∂x	PROPN
ejpam-4830	246	5	(	(	PUNCT
ejpam-4830	246	6	t	t	PROPN
ejpam-4830	246	7	,	,	PUNCT
ejpam-4830	246	8	x	x	PROPN
ejpam-4830	246	9	,	,	PUNCT
ejpam-4830	246	10	j	j	PROPN
ejpam-4830	246	11	)	)	PUNCT
ejpam-4830	246	12	≥	≥	PROPN
ejpam-4830	246	13	∂gµc	∂gµc	NOUN
ejpam-4830	246	14	∂x	∂x	PROPN
ejpam-4830	246	15	(	(	PUNCT
ejpam-4830	246	16	t	t	PROPN
ejpam-4830	246	17	,	,	PUNCT
ejpam-4830	246	18	x	x	PROPN
ejpam-4830	246	19	,	,	PUNCT
ejpam-4830	246	20	j	j	NOUN
ejpam-4830	246	21	)	)	PUNCT
ejpam-4830	247	1	=	=	SYM
ejpam-4830	247	2	gµc(t	gµc(t	PROPN
ejpam-4830	247	3	,	,	PUNCT
ejpam-4830	247	4	x2	x2	PROPN
ejpam-4830	247	5	,	,	PUNCT
ejpam-4830	247	6	j)−gµc(t	j)−gµc(t	PROPN
ejpam-4830	247	7	,	,	PUNCT
ejpam-4830	247	8	x1	x1	PROPN
ejpam-4830	247	9	,	,	PUNCT
ejpam-4830	247	10	j	j	PROPN
ejpam-4830	247	11	)	)	PUNCT
ejpam-4830	248	1	x2	x2	PROPN
ejpam-4830	248	2	−	−	PROPN
ejpam-4830	249	1	x1	x1	PROPN
ejpam-4830	249	2	≥	≥	NOUN
ejpam-4830	249	3	0	0	NUM
ejpam-4830	249	4	for	for	ADP
ejpam-4830	249	5	x1	x1	PROPN
ejpam-4830	249	6	,	,	PUNCT
ejpam-4830	249	7	x2	x2	PROPN
ejpam-4830	249	8	∈	∈	PROPN
ejpam-4830	249	9	(	(	PUNCT
ejpam-4830	249	10	0,∞	0,∞	NOUN
ejpam-4830	249	11	)	)	PUNCT
ejpam-4830	249	12	.	.	PUNCT
ejpam-4830	250	1	therefore	therefore	ADV
ejpam-4830	250	2	,	,	PUNCT
ejpam-4830	250	3	continuity	continuity	NOUN
ejpam-4830	250	4	of	of	ADP
ejpam-4830	250	5	∂gµc	∂gµc	NOUN
ejpam-4830	250	6	∂x	∂x	PROPN
ejpam-4830	250	7	(	(	PUNCT
ejpam-4830	250	8	t	t	PROPN
ejpam-4830	250	9	,	,	PUNCT
ejpam-4830	250	10	x	x	PROPN
ejpam-4830	250	11	,	,	PUNCT
ejpam-4830	250	12	j	j	PROPN
ejpam-4830	250	13	)	)	PUNCT
ejpam-4830	250	14	follows	follow	VERB
ejpam-4830	250	15	from	from	ADP
ejpam-4830	250	16	the	the	DET
ejpam-4830	250	17	continuity	continuity	NOUN
ejpam-4830	250	18	of	of	ADP
ejpam-4830	250	19	∂v	∂v	PROPN
ejpam-4830	250	20	∂x	∂x	PROPN
ejpam-4830	250	21	(	(	PUNCT
ejpam-4830	250	22	t	t	PROPN
ejpam-4830	250	23	,	,	PUNCT
ejpam-4830	250	24	x	x	PROPN
ejpam-4830	250	25	,	,	PUNCT
ejpam-4830	250	26	j	j	NOUN
ejpam-4830	250	27	)	)	PUNCT
ejpam-4830	250	28	on	on	ADP
ejpam-4830	250	29	(	(	PUNCT
ejpam-4830	250	30	0,∞	0,∞	NUM
ejpam-4830	250	31	)	)	PUNCT
ejpam-4830	250	32	.	.	PUNCT
ejpam-4830	251	1	this	this	PRON
ejpam-4830	251	2	completes	complete	VERB
ejpam-4830	251	3	our	our	PRON
ejpam-4830	251	4	proof	proof	NOUN
ejpam-4830	251	5	.	.	PUNCT
ejpam-4830	252	1	define	define	VERB
ejpam-4830	252	2	the	the	DET
ejpam-4830	252	3	infinitesimal	infinitesimal	ADJ
ejpam-4830	252	4	generator	generator	NOUN
ejpam-4830	252	5	lf(s	lf(s	X
ejpam-4830	252	6	,	,	PUNCT
ejpam-4830	252	7	x	x	X
ejpam-4830	252	8	,	,	PUNCT
ejpam-4830	252	9	αs	αs	ADJ
ejpam-4830	252	10	)	)	PUNCT
ejpam-4830	252	11	=	=	SYM
ejpam-4830	252	12	(	(	PUNCT
ejpam-4830	252	13	∂	∂	NUM
ejpam-4830	253	1	∂t	∂t	PROPN
ejpam-4830	253	2	+	+	CCONJ
ejpam-4830	253	3	rx	rx	ADJ
ejpam-4830	253	4	∂	∂	NOUN
ejpam-4830	253	5	∂x	∂x	NOUN
ejpam-4830	254	1	+	+	CCONJ
ejpam-4830	254	2	1	1	NUM
ejpam-4830	254	3	2	2	NUM
ejpam-4830	254	4	σ2(αs)x	σ2(αs)x	NOUN
ejpam-4830	254	5	2	2	NUM
ejpam-4830	254	6	∂2	∂2	NOUN
ejpam-4830	254	7	∂x2	∂x2	NOUN
ejpam-4830	254	8	−	−	NOUN
ejpam-4830	254	9	r	r	NOUN
ejpam-4830	254	10	)	)	PUNCT
ejpam-4830	254	11	f(s	f(s	ADV
ejpam-4830	254	12	,	,	PUNCT
ejpam-4830	254	13	x	x	X
ejpam-4830	254	14	,	,	PUNCT
ejpam-4830	254	15	j	j	NOUN
ejpam-4830	254	16	)	)	PUNCT
ejpam-4830	255	1	+	+	CCONJ
ejpam-4830	255	2	m∑	m∑	INTJ
ejpam-4830	255	3	i=1	i=1	PROPN
ejpam-4830	256	1	qjif(s	qjif(s	INTJ
ejpam-4830	256	2	,	,	PUNCT
ejpam-4830	256	3	x	x	PROPN
ejpam-4830	256	4	,	,	PUNCT
ejpam-4830	256	5	i	i	PROPN
ejpam-4830	256	6	)	)	PUNCT
ejpam-4830	256	7	(	(	PUNCT
ejpam-4830	256	8	34	34	NUM
ejpam-4830	256	9	)	)	PUNCT
ejpam-4830	256	10	f.	f.	PROPN
ejpam-4830	256	11	sumalpong	sumalpong	PROPN
ejpam-4830	256	12	,	,	PUNCT
ejpam-4830	256	13	m.	m.	PROPN
ejpam-4830	256	14	frondoza	frondoza	PROPN
ejpam-4830	256	15	,	,	PUNCT
ejpam-4830	256	16	n.l	n.l	PROPN
ejpam-4830	256	17	.	.	PROPN
ejpam-4830	256	18	sayson	sayson	PROPN
ejpam-4830	256	19	/	/	SYM
ejpam-4830	256	20	eur	eur	PROPN
ejpam-4830	256	21	.	.	PUNCT
ejpam-4830	257	1	j.	j.	PROPN
ejpam-4830	257	2	pure	pure	PROPN
ejpam-4830	257	3	appl	appl	PROPN
ejpam-4830	257	4	.	.	PROPN
ejpam-4830	257	5	math	math	PROPN
ejpam-4830	257	6	,	,	PUNCT
ejpam-4830	257	7	16	16	NUM
ejpam-4830	257	8	(	(	PUNCT
ejpam-4830	257	9	3	3	NUM
ejpam-4830	257	10	)	)	PUNCT
ejpam-4830	257	11	(	(	PUNCT
ejpam-4830	257	12	2023	2023	NUM
ejpam-4830	257	13	)	)	PUNCT
ejpam-4830	257	14	,	,	PUNCT
ejpam-4830	257	15	1830	1830	NUM
ejpam-4830	257	16	-	-	SYM
ejpam-4830	257	17	1847	1847	NUM
ejpam-4830	257	18	1840	1840	NUM
ejpam-4830	257	19	of	of	ADP
ejpam-4830	257	20	the	the	DET
ejpam-4830	257	21	markov	markov	NOUN
ejpam-4830	257	22	process	process	NOUN
ejpam-4830	257	23	(	(	PUNCT
ejpam-4830	257	24	xs)s∈[0,t	xs)s∈[0,t	NOUN
ejpam-4830	257	25	]	]	X
ejpam-4830	257	26	,	,	PUNCT
ejpam-4830	257	27	where	where	SCONJ
ejpam-4830	257	28	q	q	NOUN
ejpam-4830	257	29	=	=	X
ejpam-4830	257	30	(	(	PUNCT
ejpam-4830	257	31	qij)i	qij)i	PROPN
ejpam-4830	257	32	,	,	PUNCT
ejpam-4830	257	33	j=1,2,	j=1,2,	NOUN
ejpam-4830	257	34	...	...	PUNCT
ejpam-4830	257	35	,m	,m	PUNCT
ejpam-4830	257	36	is	be	AUX
ejpam-4830	257	37	the	the	DET
ejpam-4830	257	38	infinitesimal	infinitesimal	ADJ
ejpam-4830	257	39	matrix	matrix	NOUN
ejpam-4830	257	40	generator	generator	NOUN
ejpam-4830	257	41	of	of	ADP
ejpam-4830	257	42	the	the	DET
ejpam-4830	257	43	markov	markov	NOUN
ejpam-4830	257	44	process	process	NOUN
ejpam-4830	257	45	(	(	PUNCT
ejpam-4830	257	46	αs)s∈[0,t	αs)s∈[0,t	NOUN
ejpam-4830	257	47	]	]	X
ejpam-4830	257	48	,	,	PUNCT
ejpam-4830	257	49	for	for	ADP
ejpam-4830	257	50	any	any	DET
ejpam-4830	257	51	sufficiently	sufficiently	ADV
ejpam-4830	257	52	differentiable	differentiable	ADJ
ejpam-4830	257	53	function	function	NOUN
ejpam-4830	257	54	f	f	PROPN
ejpam-4830	257	55	of	of	ADP
ejpam-4830	257	56	(	(	PUNCT
ejpam-4830	257	57	s	s	PROPN
ejpam-4830	257	58	,	,	PUNCT
ejpam-4830	257	59	x	x	NOUN
ejpam-4830	257	60	,	,	PUNCT
ejpam-4830	257	61	j	j	NOUN
ejpam-4830	257	62	)	)	PUNCT
ejpam-4830	257	63	∈	∈	PROPN
ejpam-4830	258	1	[	[	X
ejpam-4830	258	2	0	0	NUM
ejpam-4830	258	3	,	,	PUNCT
ejpam-4830	258	4	t	t	X
ejpam-4830	258	5	]	]	X
ejpam-4830	258	6	×	×	NOUN
ejpam-4830	258	7	(	(	PUNCT
ejpam-4830	258	8	0,∞)×m	0,∞)×m	PROPN
ejpam-4830	258	9	.	.	PUNCT
ejpam-4830	259	1	lemma	lemma	PROPN
ejpam-4830	259	2	5	5	NUM
ejpam-4830	259	3	.	.	PUNCT
ejpam-4830	260	1	for	for	ADP
ejpam-4830	260	2	all	all	DET
ejpam-4830	260	3	(	(	PUNCT
ejpam-4830	260	4	t	t	PROPN
ejpam-4830	260	5	,	,	PUNCT
ejpam-4830	260	6	x	x	PROPN
ejpam-4830	260	7	,	,	PUNCT
ejpam-4830	260	8	j	j	NOUN
ejpam-4830	260	9	)	)	PUNCT
ejpam-4830	260	10	∈	∈	PROPN
ejpam-4830	261	1	[	[	X
ejpam-4830	261	2	0	0	NUM
ejpam-4830	261	3	,	,	PUNCT
ejpam-4830	261	4	t	t	X
ejpam-4830	261	5	]	]	X
ejpam-4830	261	6	×	×	NOUN
ejpam-4830	261	7	(	(	PUNCT
ejpam-4830	261	8	0,∞)×m	0,∞)×m	ADJ
ejpam-4830	261	9	,	,	PUNCT
ejpam-4830	261	10	we	we	PRON
ejpam-4830	261	11	have	have	AUX
ejpam-4830	261	12	lgµc(t	lgµc(t	PROPN
ejpam-4830	261	13	,	,	PUNCT
ejpam-4830	261	14	x	x	PROPN
ejpam-4830	261	15	,	,	PUNCT
ejpam-4830	261	16	j	j	PROPN
ejpam-4830	261	17	)	)	PUNCT
ejpam-4830	261	18	<	<	X
ejpam-4830	261	19	0	0	PUNCT
ejpam-4830	261	20	(	(	PUNCT
ejpam-4830	261	21	35	35	NUM
ejpam-4830	261	22	)	)	PUNCT
ejpam-4830	261	23	when	when	SCONJ
ejpam-4830	261	24	the	the	DET
ejpam-4830	261	25	contract	contract	NOUN
ejpam-4830	261	26	drift	drift	NOUN
ejpam-4830	261	27	µc	µc	AUX
ejpam-4830	261	28	satisfies	satisfy	VERB
ejpam-4830	261	29	µc	µc	ADP
ejpam-4830	261	30	<	<	X
ejpam-4830	261	31	r.	r.	PROPN
ejpam-4830	261	32	proof	proof	NOUN
ejpam-4830	261	33	.	.	PUNCT
ejpam-4830	262	1	the	the	DET
ejpam-4830	262	2	payoff	payoff	NOUN
ejpam-4830	262	3	function	function	NOUN
ejpam-4830	262	4	in	in	ADP
ejpam-4830	262	5	(	(	PUNCT
ejpam-4830	262	6	14	14	NUM
ejpam-4830	262	7	)	)	PUNCT
ejpam-4830	262	8	can	can	AUX
ejpam-4830	262	9	be	be	AUX
ejpam-4830	262	10	rewritten	rewrite	VERB
ejpam-4830	262	11	as	as	ADP
ejpam-4830	262	12	gµc(t	gµc(t	PROPN
ejpam-4830	262	13	,	,	PUNCT
ejpam-4830	262	14	x	x	NOUN
ejpam-4830	262	15	,	,	PUNCT
ejpam-4830	262	16	j	j	NOUN
ejpam-4830	262	17	)	)	PUNCT
ejpam-4830	262	18	=	=	PUNCT
ejpam-4830	263	1	eµc	eµc	PROPN
ejpam-4830	264	1	[	[	X
ejpam-4830	264	2	(	(	PUNCT
ejpam-4830	264	3	k	k	NOUN
ejpam-4830	264	4	−xt	−xt	PROPN
ejpam-4830	264	5	)	)	PUNCT
ejpam-4830	265	1	+	+	NUM
ejpam-4830	265	2	∣∣xt	∣∣xt	X
ejpam-4830	265	3	=	=	SYM
ejpam-4830	265	4	x	x	PROPN
ejpam-4830	265	5	,	,	PUNCT
ejpam-4830	265	6	αt	αt	PROPN
ejpam-4830	265	7	=	=	SYM
ejpam-4830	265	8	j	j	PROPN
ejpam-4830	265	9	]	]	X
ejpam-4830	265	10	for	for	ADP
ejpam-4830	265	11	all	all	DET
ejpam-4830	265	12	j	j	PROPN
ejpam-4830	265	13	∈	∈	PROPN
ejpam-4830	265	14	m	m	VERB
ejpam-4830	265	15	and	and	CCONJ
ejpam-4830	265	16	hence	hence	ADV
ejpam-4830	265	17	a	a	DET
ejpam-4830	265	18	martingale	martingale	NOUN
ejpam-4830	265	19	by	by	ADP
ejpam-4830	265	20	tower	tower	NOUN
ejpam-4830	265	21	property	property	NOUN
ejpam-4830	265	22	.	.	PUNCT
ejpam-4830	266	1	by	by	ADP
ejpam-4830	266	2	(	(	PUNCT
ejpam-4830	266	3	7	7	NUM
ejpam-4830	266	4	)	)	PUNCT
ejpam-4830	266	5	and	and	CCONJ
ejpam-4830	266	6	the	the	DET
ejpam-4830	266	7	itô	itô	PROPN
ejpam-4830	266	8	’s	’s	PART
ejpam-4830	266	9	formula	formula	NOUN
ejpam-4830	266	10	we	we	PRON
ejpam-4830	266	11	have	have	VERB
ejpam-4830	266	12	dgµc(t	dgµc(t	PROPN
ejpam-4830	266	13	,	,	PUNCT
ejpam-4830	266	14	x	x	NOUN
ejpam-4830	266	15	,	,	PUNCT
ejpam-4830	266	16	j	j	NOUN
ejpam-4830	266	17	)	)	PUNCT
ejpam-4830	266	18	=	=	SYM
ejpam-4830	266	19	∂gµc	∂gµc	PRON
ejpam-4830	266	20	∂t	∂t	PROPN
ejpam-4830	266	21	(	(	PUNCT
ejpam-4830	266	22	t	t	PROPN
ejpam-4830	266	23	,	,	PUNCT
ejpam-4830	266	24	x	x	PROPN
ejpam-4830	266	25	,	,	PUNCT
ejpam-4830	266	26	j	j	PROPN
ejpam-4830	266	27	)	)	PUNCT
ejpam-4830	266	28	+	+	CCONJ
ejpam-4830	266	29	µcx	µcx	NOUN
ejpam-4830	266	30	∂gµc	∂gµc	ADJ
ejpam-4830	266	31	∂x	∂x	PROPN
ejpam-4830	266	32	(	(	PUNCT
ejpam-4830	266	33	t	t	PROPN
ejpam-4830	266	34	,	,	PUNCT
ejpam-4830	266	35	x	x	PROPN
ejpam-4830	266	36	,	,	PUNCT
ejpam-4830	266	37	j	j	PROPN
ejpam-4830	266	38	)	)	PUNCT
ejpam-4830	266	39	+	+	CCONJ
ejpam-4830	266	40	1	1	NUM
ejpam-4830	266	41	2	2	NUM
ejpam-4830	266	42	σ2(j)x2	σ2(j)x2	NOUN
ejpam-4830	266	43	∂2gµc	∂2gµc	NOUN
ejpam-4830	266	44	∂x2	∂x2	NOUN
ejpam-4830	266	45	(	(	PUNCT
ejpam-4830	266	46	t	t	PROPN
ejpam-4830	266	47	,	,	PUNCT
ejpam-4830	266	48	x	x	PROPN
ejpam-4830	266	49	,	,	PUNCT
ejpam-4830	266	50	j	j	NOUN
ejpam-4830	266	51	)	)	PUNCT
ejpam-4830	266	52	+	+	CCONJ
ejpam-4830	266	53	m∑	m∑	CCONJ
ejpam-4830	266	54	i=1	i=1	PROPN
ejpam-4830	266	55	qjig	qjig	PROPN
ejpam-4830	266	56	µc(t	µc(t	PROPN
ejpam-4830	266	57	,	,	PUNCT
ejpam-4830	266	58	x	x	PRON
ejpam-4830	266	59	,	,	PUNCT
ejpam-4830	266	60	i	i	NOUN
ejpam-4830	266	61	)	)	PUNCT
ejpam-4830	266	62	+	+	CCONJ
ejpam-4830	266	63	σ(j)x	σ(j)x	PROPN
ejpam-4830	266	64	∂gµc	∂gµc	NOUN
ejpam-4830	266	65	∂x	∂x	PROPN
ejpam-4830	266	66	dwµc	dwµc	NOUN
ejpam-4830	266	67	t	t	NOUN
ejpam-4830	266	68	.	.	PUNCT
ejpam-4830	267	1	since	since	SCONJ
ejpam-4830	267	2	gµc(t	gµc(t	PROPN
ejpam-4830	267	3	,	,	PUNCT
ejpam-4830	267	4	x	x	NOUN
ejpam-4830	267	5	,	,	PUNCT
ejpam-4830	267	6	j	j	NOUN
ejpam-4830	267	7	)	)	PUNCT
ejpam-4830	267	8	is	be	AUX
ejpam-4830	267	9	a	a	DET
ejpam-4830	267	10	martingale	martingale	NOUN
ejpam-4830	267	11	,	,	PUNCT
ejpam-4830	267	12	we	we	PRON
ejpam-4830	267	13	find	find	VERB
ejpam-4830	267	14	∂gµc	∂gµc	ADJ
ejpam-4830	267	15	∂t	∂t	PROPN
ejpam-4830	267	16	(	(	PUNCT
ejpam-4830	267	17	t	t	PROPN
ejpam-4830	267	18	,	,	PUNCT
ejpam-4830	267	19	x	x	PROPN
ejpam-4830	267	20	,	,	PUNCT
ejpam-4830	267	21	j	j	PROPN
ejpam-4830	267	22	)	)	PUNCT
ejpam-4830	267	23	+	+	CCONJ
ejpam-4830	267	24	µcx	µcx	NOUN
ejpam-4830	267	25	∂gµc	∂gµc	ADJ
ejpam-4830	267	26	∂x	∂x	PROPN
ejpam-4830	267	27	(	(	PUNCT
ejpam-4830	267	28	t	t	PROPN
ejpam-4830	267	29	,	,	PUNCT
ejpam-4830	267	30	x	x	PROPN
ejpam-4830	267	31	,	,	PUNCT
ejpam-4830	267	32	j	j	PROPN
ejpam-4830	267	33	)	)	PUNCT
ejpam-4830	268	1	+	+	CCONJ
ejpam-4830	268	2	1	1	NUM
ejpam-4830	268	3	2	2	NUM
ejpam-4830	268	4	σ2(j)x2	σ2(j)x2	NOUN
ejpam-4830	268	5	∂2gµc	∂2gµc	NOUN
ejpam-4830	268	6	∂x2	∂x2	NOUN
ejpam-4830	268	7	(	(	PUNCT
ejpam-4830	268	8	t	t	PROPN
ejpam-4830	268	9	,	,	PUNCT
ejpam-4830	268	10	x	x	PROPN
ejpam-4830	268	11	,	,	PUNCT
ejpam-4830	268	12	j	j	NOUN
ejpam-4830	268	13	)	)	PUNCT
ejpam-4830	269	1	+	+	CCONJ
ejpam-4830	269	2	m∑	m∑	CCONJ
ejpam-4830	269	3	i=1	i=1	PROPN
ejpam-4830	269	4	qjig	qjig	PROPN
ejpam-4830	269	5	µc(t	µc(t	PROPN
ejpam-4830	269	6	,	,	PUNCT
ejpam-4830	269	7	x	x	PRON
ejpam-4830	269	8	,	,	PUNCT
ejpam-4830	269	9	i	i	NOUN
ejpam-4830	269	10	)	)	PUNCT
ejpam-4830	270	1	=	=	PUNCT
ejpam-4830	270	2	0	0	X
ejpam-4830	270	3	.	.	PUNCT
ejpam-4830	271	1	(	(	PUNCT
ejpam-4830	271	2	36	36	NUM
ejpam-4830	271	3	)	)	PUNCT
ejpam-4830	271	4	substituting	substituting	NOUN
ejpam-4830	271	5	(	(	PUNCT
ejpam-4830	271	6	36	36	NUM
ejpam-4830	271	7	)	)	PUNCT
ejpam-4830	271	8	to	to	ADP
ejpam-4830	271	9	(	(	PUNCT
ejpam-4830	271	10	34	34	NUM
ejpam-4830	271	11	)	)	PUNCT
ejpam-4830	271	12	we	we	PRON
ejpam-4830	271	13	have	have	VERB
ejpam-4830	271	14	lgµc(t	lgµc(t	PROPN
ejpam-4830	271	15	,	,	PUNCT
ejpam-4830	271	16	x	x	PROPN
ejpam-4830	271	17	,	,	PUNCT
ejpam-4830	271	18	j	j	NOUN
ejpam-4830	271	19	)	)	PUNCT
ejpam-4830	271	20	=	=	PUNCT
ejpam-4830	272	1	(	(	PUNCT
ejpam-4830	272	2	r	r	NOUN
ejpam-4830	272	3	−	−	PROPN
ejpam-4830	272	4	µc)x	µc)x	NUM
ejpam-4830	272	5	∂gµc	∂gµc	NOUN
ejpam-4830	272	6	∂x	∂x	PROPN
ejpam-4830	272	7	(	(	PUNCT
ejpam-4830	272	8	t	t	PROPN
ejpam-4830	272	9	,	,	PUNCT
ejpam-4830	272	10	x	x	X
ejpam-4830	272	11	,	,	PUNCT
ejpam-4830	272	12	j)−	j)−	PROPN
ejpam-4830	272	13	rgµc(t	rgµc(t	PROPN
ejpam-4830	272	14	,	,	PUNCT
ejpam-4830	272	15	x	x	PROPN
ejpam-4830	272	16	,	,	PUNCT
ejpam-4830	272	17	j	j	PROPN
ejpam-4830	272	18	)	)	PUNCT
ejpam-4830	272	19	.	.	PUNCT
ejpam-4830	273	1	(	(	PUNCT
ejpam-4830	273	2	37	37	NUM
ejpam-4830	273	3	)	)	PUNCT
ejpam-4830	273	4	since	since	SCONJ
ejpam-4830	273	5	gµc(t	gµc(t	PROPN
ejpam-4830	273	6	,	,	PUNCT
ejpam-4830	273	7	x	x	NOUN
ejpam-4830	273	8	,	,	PUNCT
ejpam-4830	273	9	j	j	NOUN
ejpam-4830	273	10	)	)	PUNCT
ejpam-4830	273	11	is	be	AUX
ejpam-4830	273	12	convex	convex	ADJ
ejpam-4830	273	13	and	and	CCONJ
ejpam-4830	273	14	decreasing	decrease	VERB
ejpam-4830	273	15	with	with	ADP
ejpam-4830	273	16	respect	respect	NOUN
ejpam-4830	273	17	to	to	ADP
ejpam-4830	273	18	x	x	SYM
ejpam-4830	273	19	∈	∈	PROPN
ejpam-4830	273	20	(	(	PUNCT
ejpam-4830	273	21	0,∞	0,∞	NOUN
ejpam-4830	273	22	)	)	PUNCT
ejpam-4830	273	23	,	,	PUNCT
ejpam-4830	273	24	then	then	ADV
ejpam-4830	273	25	we	we	PRON
ejpam-4830	273	26	have	have	VERB
ejpam-4830	273	27	∂gµc	∂gµc	NOUN
ejpam-4830	273	28	∂x	∂x	PROPN
ejpam-4830	273	29	(	(	PUNCT
ejpam-4830	273	30	t	t	PROPN
ejpam-4830	273	31	,	,	PUNCT
ejpam-4830	273	32	x	x	PROPN
ejpam-4830	273	33	,	,	PUNCT
ejpam-4830	273	34	j	j	PROPN
ejpam-4830	273	35	)	)	PUNCT
ejpam-4830	273	36	<	<	X
ejpam-4830	274	1	0	0	X
ejpam-4830	274	2	.	.	PUNCT
ejpam-4830	275	1	this	this	PRON
ejpam-4830	275	2	completes	complete	VERB
ejpam-4830	275	3	our	our	PRON
ejpam-4830	275	4	proof	proof	NOUN
ejpam-4830	275	5	.	.	PUNCT
ejpam-4830	276	1	lemma	lemma	PROPN
ejpam-4830	276	2	6	6	NUM
ejpam-4830	276	3	.	.	PUNCT
ejpam-4830	277	1	for	for	ADP
ejpam-4830	277	2	all	all	PRON
ejpam-4830	277	3	(	(	PUNCT
ejpam-4830	277	4	t	t	PROPN
ejpam-4830	277	5	,	,	PUNCT
ejpam-4830	277	6	y	y	PROPN
ejpam-4830	277	7	,	,	PUNCT
ejpam-4830	277	8	j	j	PROPN
ejpam-4830	277	9	)	)	PUNCT
ejpam-4830	277	10	∈	∈	PROPN
ejpam-4830	277	11	c	c	X
ejpam-4830	277	12	,	,	PUNCT
ejpam-4830	277	13	we	we	PRON
ejpam-4830	277	14	have	have	VERB
ejpam-4830	277	15	∂v	∂v	PROPN
ejpam-4830	277	16	∂y	∂y	SYM
ejpam-4830	277	17	(	(	PUNCT
ejpam-4830	277	18	t	t	PROPN
ejpam-4830	277	19	,	,	PUNCT
ejpam-4830	277	20	y	y	PROPN
ejpam-4830	277	21	,	,	PUNCT
ejpam-4830	277	22	j	j	PROPN
ejpam-4830	277	23	)	)	PUNCT
ejpam-4830	277	24	>	>	X
ejpam-4830	277	25	∂gµc	∂gµc	X
ejpam-4830	277	26	∂y	∂y	SYM
ejpam-4830	277	27	(	(	PUNCT
ejpam-4830	277	28	t	t	PROPN
ejpam-4830	277	29	,	,	PUNCT
ejpam-4830	277	30	y	y	PROPN
ejpam-4830	277	31	,	,	PUNCT
ejpam-4830	277	32	j	j	PROPN
ejpam-4830	277	33	)	)	PUNCT
ejpam-4830	277	34	.	.	PUNCT
ejpam-4830	278	1	(	(	PUNCT
ejpam-4830	278	2	38	38	NUM
ejpam-4830	278	3	)	)	PUNCT
ejpam-4830	278	4	proof	proof	NOUN
ejpam-4830	278	5	.	.	PUNCT
ejpam-4830	279	1	let	let	AUX
ejpam-4830	279	2	(	(	PUNCT
ejpam-4830	279	3	t	t	PROPN
ejpam-4830	279	4	,	,	PUNCT
ejpam-4830	279	5	xb	xb	PROPN
ejpam-4830	279	6	,	,	PUNCT
ejpam-4830	279	7	j	j	PROPN
ejpam-4830	279	8	)	)	PUNCT
ejpam-4830	279	9	be	be	VERB
ejpam-4830	279	10	a	a	DET
ejpam-4830	279	11	fixed	fix	VERB
ejpam-4830	279	12	point	point	NOUN
ejpam-4830	279	13	on	on	ADP
ejpam-4830	279	14	the	the	DET
ejpam-4830	279	15	boundary	boundary	ADJ
ejpam-4830	279	16	function	function	NOUN
ejpam-4830	279	17	bd(t	bd(t	PROPN
ejpam-4830	279	18	,	,	PUNCT
ejpam-4830	279	19	j	j	NOUN
ejpam-4830	279	20	)	)	PUNCT
ejpam-4830	279	21	so	so	SCONJ
ejpam-4830	279	22	that	that	SCONJ
ejpam-4830	279	23	xb	xb	PROPN
ejpam-4830	279	24	=	=	SYM
ejpam-4830	279	25	bd(t	bd(t	PROPN
ejpam-4830	279	26	,	,	PUNCT
ejpam-4830	279	27	j	j	NOUN
ejpam-4830	279	28	)	)	PUNCT
ejpam-4830	279	29	.	.	PUNCT
ejpam-4830	280	1	let	let	VERB
ejpam-4830	280	2	xb	xb	X
ejpam-4830	280	3	<	<	X
ejpam-4830	280	4	y	y	PROPN
ejpam-4830	280	5	≤	≤	PROPN
ejpam-4830	281	1	k	k	PROPN
ejpam-4830	282	1	so	so	SCONJ
ejpam-4830	282	2	that	that	SCONJ
ejpam-4830	282	3	(	(	PUNCT
ejpam-4830	282	4	t	t	PROPN
ejpam-4830	282	5	,	,	PUNCT
ejpam-4830	282	6	y	y	PROPN
ejpam-4830	282	7	,	,	PUNCT
ejpam-4830	282	8	j	j	PROPN
ejpam-4830	282	9	)	)	PUNCT
ejpam-4830	282	10	∈	∈	PROPN
ejpam-4830	282	11	c.	c.	NOUN
ejpam-4830	282	12	since	since	SCONJ
ejpam-4830	282	13	x	x	PROPN
ejpam-4830	282	14	7→	7→	NUM
ejpam-4830	282	15	v	v	NOUN
ejpam-4830	282	16	(	(	PUNCT
ejpam-4830	282	17	t	t	PROPN
ejpam-4830	282	18	,	,	PUNCT
ejpam-4830	282	19	x	x	PROPN
ejpam-4830	282	20	,	,	PUNCT
ejpam-4830	282	21	j	j	NOUN
ejpam-4830	282	22	)	)	PUNCT
ejpam-4830	282	23	is	be	AUX
ejpam-4830	282	24	continuous	continuous	ADJ
ejpam-4830	282	25	on	on	ADP
ejpam-4830	282	26	(	(	PUNCT
ejpam-4830	282	27	0,∞	0,∞	NOUN
ejpam-4830	282	28	)	)	PUNCT
ejpam-4830	282	29	f.	f.	PROPN
ejpam-4830	282	30	sumalpong	sumalpong	PROPN
ejpam-4830	282	31	,	,	PUNCT
ejpam-4830	282	32	m.	m.	PROPN
ejpam-4830	282	33	frondoza	frondoza	PROPN
ejpam-4830	282	34	,	,	PUNCT
ejpam-4830	282	35	n.l	n.l	PROPN
ejpam-4830	282	36	.	.	PROPN
ejpam-4830	282	37	sayson	sayson	PROPN
ejpam-4830	282	38	/	/	SYM
ejpam-4830	282	39	eur	eur	PROPN
ejpam-4830	282	40	.	.	PUNCT
ejpam-4830	283	1	j.	j.	PROPN
ejpam-4830	283	2	pure	pure	PROPN
ejpam-4830	283	3	appl	appl	PROPN
ejpam-4830	283	4	.	.	PROPN
ejpam-4830	283	5	math	math	PROPN
ejpam-4830	283	6	,	,	PUNCT
ejpam-4830	283	7	16	16	NUM
ejpam-4830	283	8	(	(	PUNCT
ejpam-4830	283	9	3	3	NUM
ejpam-4830	283	10	)	)	PUNCT
ejpam-4830	283	11	(	(	PUNCT
ejpam-4830	283	12	2023	2023	NUM
ejpam-4830	283	13	)	)	PUNCT
ejpam-4830	283	14	,	,	PUNCT
ejpam-4830	283	15	1830	1830	NUM
ejpam-4830	283	16	-	-	SYM
ejpam-4830	283	17	1847	1847	NUM
ejpam-4830	283	18	1841	1841	NUM
ejpam-4830	283	19	by	by	ADP
ejpam-4830	283	20	lemma	lemma	PROPN
ejpam-4830	283	21	2	2	NUM
ejpam-4830	283	22	and	and	CCONJ
ejpam-4830	283	23	differentiable	differentiable	VERB
ejpam-4830	283	24	p	p	NOUN
ejpam-4830	283	25	-	-	PUNCT
ejpam-4830	283	26	almost	almost	ADV
ejpam-4830	283	27	surely	surely	ADV
ejpam-4830	283	28	,	,	PUNCT
ejpam-4830	283	29	by	by	ADP
ejpam-4830	283	30	mean	mean	NOUN
ejpam-4830	283	31	value	value	NOUN
ejpam-4830	283	32	theorem	theorem	VERB
ejpam-4830	283	33	,	,	PUNCT
ejpam-4830	283	34	there	there	PRON
ejpam-4830	283	35	exists	exist	VERB
ejpam-4830	283	36	at	at	ADP
ejpam-4830	283	37	least	least	ADJ
ejpam-4830	283	38	one	one	NUM
ejpam-4830	283	39	c	c	NOUN
ejpam-4830	283	40	∈	∈	PROPN
ejpam-4830	283	41	(	(	PUNCT
ejpam-4830	283	42	xb	xb	PROPN
ejpam-4830	283	43	,	,	PUNCT
ejpam-4830	283	44	y	y	PROPN
ejpam-4830	283	45	)	)	PUNCT
ejpam-4830	283	46	such	such	ADJ
ejpam-4830	283	47	that	that	PRON
ejpam-4830	283	48	v	v	NOUN
ejpam-4830	283	49	(	(	PUNCT
ejpam-4830	283	50	t	t	PROPN
ejpam-4830	283	51	,	,	PUNCT
ejpam-4830	283	52	y	y	PROPN
ejpam-4830	283	53	,	,	PUNCT
ejpam-4830	283	54	j)−	j)−	PROPN
ejpam-4830	283	55	v	v	PROPN
ejpam-4830	283	56	(	(	PUNCT
ejpam-4830	283	57	t	t	PROPN
ejpam-4830	283	58	,	,	PUNCT
ejpam-4830	283	59	xb	xb	PROPN
ejpam-4830	283	60	,	,	PUNCT
ejpam-4830	283	61	j	j	PROPN
ejpam-4830	283	62	)	)	PUNCT
ejpam-4830	283	63	y	y	PROPN
ejpam-4830	283	64	−	−	NOUN
ejpam-4830	283	65	xb	xb	X
ejpam-4830	284	1	=	=	PUNCT
ejpam-4830	284	2	∂v	∂v	PROPN
ejpam-4830	284	3	∂x	∂x	PROPN
ejpam-4830	284	4	(	(	PUNCT
ejpam-4830	284	5	t	t	PROPN
ejpam-4830	284	6	,	,	PUNCT
ejpam-4830	284	7	c	c	X
ejpam-4830	284	8	,	,	PUNCT
ejpam-4830	284	9	j	j	PROPN
ejpam-4830	284	10	)	)	PUNCT
ejpam-4830	284	11	.	.	PUNCT
ejpam-4830	285	1	similarly	similarly	ADV
ejpam-4830	285	2	,	,	PUNCT
ejpam-4830	285	3	we	we	PRON
ejpam-4830	285	4	have	have	VERB
ejpam-4830	285	5	gµc(t	gµc(t	PROPN
ejpam-4830	285	6	,	,	PUNCT
ejpam-4830	285	7	y	y	PROPN
ejpam-4830	285	8	,	,	PUNCT
ejpam-4830	285	9	j)−gµc(t	j)−gµc(t	PROPN
ejpam-4830	285	10	,	,	PUNCT
ejpam-4830	285	11	xb	xb	PROPN
ejpam-4830	285	12	,	,	PUNCT
ejpam-4830	285	13	j	j	PROPN
ejpam-4830	285	14	)	)	PUNCT
ejpam-4830	285	15	y	y	PROPN
ejpam-4830	285	16	−	−	PROPN
ejpam-4830	285	17	xb	xb	PROPN
ejpam-4830	285	18	=	=	SYM
ejpam-4830	285	19	∂gµc	∂gµc	X
ejpam-4830	285	20	∂x	∂x	PROPN
ejpam-4830	285	21	(	(	PUNCT
ejpam-4830	285	22	t	t	PROPN
ejpam-4830	285	23	,	,	PUNCT
ejpam-4830	285	24	c	c	X
ejpam-4830	285	25	,	,	PUNCT
ejpam-4830	285	26	j	j	PROPN
ejpam-4830	285	27	)	)	PUNCT
ejpam-4830	285	28	.	.	PUNCT
ejpam-4830	286	1	since	since	SCONJ
ejpam-4830	286	2	v	v	NUM
ejpam-4830	286	3	(	(	PUNCT
ejpam-4830	286	4	t	t	PROPN
ejpam-4830	286	5	,	,	PUNCT
ejpam-4830	286	6	y	y	PROPN
ejpam-4830	286	7	,	,	PUNCT
ejpam-4830	286	8	j	j	PROPN
ejpam-4830	286	9	)	)	PUNCT
ejpam-4830	286	10	>	>	X
ejpam-4830	286	11	gµc(t	gµc(t	PROPN
ejpam-4830	286	12	,	,	PUNCT
ejpam-4830	286	13	y	y	PROPN
ejpam-4830	286	14	,	,	PUNCT
ejpam-4830	286	15	j	j	PROPN
ejpam-4830	286	16	)	)	PUNCT
ejpam-4830	286	17	for	for	ADP
ejpam-4830	286	18	all	all	DET
ejpam-4830	286	19	(	(	PUNCT
ejpam-4830	286	20	t	t	PROPN
ejpam-4830	286	21	,	,	PUNCT
ejpam-4830	286	22	y	y	PROPN
ejpam-4830	286	23	,	,	PUNCT
ejpam-4830	286	24	j	j	PROPN
ejpam-4830	286	25	)	)	PUNCT
ejpam-4830	286	26	∈	∈	PROPN
ejpam-4830	286	27	c	c	X
ejpam-4830	286	28	,	,	PUNCT
ejpam-4830	286	29	we	we	PRON
ejpam-4830	286	30	have	have	VERB
ejpam-4830	286	31	∂v	∂v	PROPN
ejpam-4830	286	32	∂x	∂x	PROPN
ejpam-4830	286	33	(	(	PUNCT
ejpam-4830	286	34	t	t	PROPN
ejpam-4830	286	35	,	,	PUNCT
ejpam-4830	286	36	c	c	X
ejpam-4830	286	37	,	,	PUNCT
ejpam-4830	286	38	j	j	NOUN
ejpam-4830	286	39	)	)	PUNCT
ejpam-4830	287	1	=	=	SYM
ejpam-4830	287	2	v	v	X
ejpam-4830	287	3	(	(	PUNCT
ejpam-4830	287	4	t	t	PROPN
ejpam-4830	287	5	,	,	PUNCT
ejpam-4830	287	6	y	y	PROPN
ejpam-4830	287	7	,	,	PUNCT
ejpam-4830	287	8	j)−	j)−	PROPN
ejpam-4830	287	9	v	v	PROPN
ejpam-4830	287	10	(	(	PUNCT
ejpam-4830	287	11	t	t	PROPN
ejpam-4830	287	12	,	,	PUNCT
ejpam-4830	287	13	xb	xb	PROPN
ejpam-4830	287	14	,	,	PUNCT
ejpam-4830	287	15	j	j	PROPN
ejpam-4830	287	16	)	)	PUNCT
ejpam-4830	287	17	y	y	PROPN
ejpam-4830	287	18	−	−	PROPN
ejpam-4830	287	19	xb	xb	PROPN
ejpam-4830	287	20	>	>	X
ejpam-4830	287	21	gµc(t	gµc(t	PROPN
ejpam-4830	287	22	,	,	PUNCT
ejpam-4830	287	23	y	y	PROPN
ejpam-4830	287	24	,	,	PUNCT
ejpam-4830	287	25	j)−gµc(t	j)−gµc(t	PROPN
ejpam-4830	287	26	,	,	PUNCT
ejpam-4830	287	27	xb	xb	PROPN
ejpam-4830	287	28	,	,	PUNCT
ejpam-4830	287	29	j	j	PROPN
ejpam-4830	287	30	)	)	PUNCT
ejpam-4830	287	31	y	y	PROPN
ejpam-4830	287	32	−	−	PROPN
ejpam-4830	287	33	xb	xb	PROPN
ejpam-4830	287	34	=	=	SYM
ejpam-4830	287	35	∂gµc	∂gµc	X
ejpam-4830	287	36	∂x	∂x	PROPN
ejpam-4830	287	37	(	(	PUNCT
ejpam-4830	287	38	t	t	PROPN
ejpam-4830	287	39	,	,	PUNCT
ejpam-4830	287	40	c	c	X
ejpam-4830	287	41	,	,	PUNCT
ejpam-4830	287	42	j	j	PROPN
ejpam-4830	287	43	)	)	PUNCT
ejpam-4830	287	44	.	.	PUNCT
ejpam-4830	288	1	since	since	SCONJ
ejpam-4830	288	2	v	v	NOUN
ejpam-4830	288	3	and	and	CCONJ
ejpam-4830	288	4	gµc	gµc	NOUN
ejpam-4830	288	5	are	be	AUX
ejpam-4830	288	6	continuous	continuous	ADJ
ejpam-4830	288	7	and	and	CCONJ
ejpam-4830	288	8	convex	convex	PROPN
ejpam-4830	288	9	,	,	PUNCT
ejpam-4830	288	10	the	the	DET
ejpam-4830	288	11	above	above	ADJ
ejpam-4830	288	12	inequality	inequality	NOUN
ejpam-4830	288	13	holds	hold	VERB
ejpam-4830	288	14	for	for	ADP
ejpam-4830	288	15	all	all	PRON
ejpam-4830	288	16	(	(	PUNCT
ejpam-4830	288	17	t	t	PROPN
ejpam-4830	288	18	,	,	PUNCT
ejpam-4830	288	19	c	c	X
ejpam-4830	288	20	,	,	PUNCT
ejpam-4830	288	21	j	j	NOUN
ejpam-4830	288	22	)	)	PUNCT
ejpam-4830	288	23	∈	∈	PROPN
ejpam-4830	288	24	c.	c.	PROPN
ejpam-4830	288	25	lemma	lemma	PROPN
ejpam-4830	288	26	7	7	NUM
ejpam-4830	288	27	.	.	X
ejpam-4830	288	28	for	for	ADP
ejpam-4830	288	29	any	any	DET
ejpam-4830	288	30	(	(	PUNCT
ejpam-4830	288	31	t	t	PROPN
ejpam-4830	288	32	,	,	PUNCT
ejpam-4830	288	33	x	x	NOUN
ejpam-4830	288	34	,	,	PUNCT
ejpam-4830	288	35	j	j	NOUN
ejpam-4830	288	36	)	)	PUNCT
ejpam-4830	288	37	in	in	ADP
ejpam-4830	288	38	the	the	DET
ejpam-4830	288	39	optimal	optimal	ADJ
ejpam-4830	288	40	stopping	stopping	NOUN
ejpam-4830	288	41	boundary	boundary	NOUN
ejpam-4830	288	42	∂c	∂c	PROPN
ejpam-4830	289	1	⊂	⊂	PROPN
ejpam-4830	289	2	d	d	X
ejpam-4830	289	3	,	,	PUNCT
ejpam-4830	289	4	we	we	PRON
ejpam-4830	289	5	have	have	VERB
ejpam-4830	289	6	∂v	∂v	PROPN
ejpam-4830	289	7	∂x	∂x	PROPN
ejpam-4830	289	8	(	(	PUNCT
ejpam-4830	289	9	t	t	PROPN
ejpam-4830	289	10	,	,	PUNCT
ejpam-4830	289	11	x+	x+	PROPN
ejpam-4830	289	12	,	,	PUNCT
ejpam-4830	289	13	j	j	NOUN
ejpam-4830	289	14	)	)	PUNCT
ejpam-4830	290	1	=	=	PUNCT
ejpam-4830	290	2	∂v	∂v	PROPN
ejpam-4830	290	3	∂x	∂x	PROPN
ejpam-4830	290	4	(	(	PUNCT
ejpam-4830	290	5	t	t	PROPN
ejpam-4830	290	6	,	,	PUNCT
ejpam-4830	290	7	x−	x−	PROPN
ejpam-4830	290	8	,	,	PUNCT
ejpam-4830	290	9	j	j	PROPN
ejpam-4830	290	10	)	)	PUNCT
ejpam-4830	290	11	.	.	PUNCT
ejpam-4830	291	1	(	(	PUNCT
ejpam-4830	291	2	39	39	NUM
ejpam-4830	291	3	)	)	PUNCT
ejpam-4830	291	4	proof	proof	NOUN
ejpam-4830	291	5	.	.	PUNCT
ejpam-4830	292	1	for	for	ADP
ejpam-4830	292	2	nay	nay	PROPN
ejpam-4830	292	3	ϵ	ϵ	X
ejpam-4830	292	4	>	>	X
ejpam-4830	292	5	0	0	NUM
ejpam-4830	292	6	,	,	PUNCT
ejpam-4830	292	7	consider	consider	VERB
ejpam-4830	292	8	the	the	DET
ejpam-4830	292	9	stopping	stopping	NOUN
ejpam-4830	292	10	time	time	NOUN
ejpam-4830	292	11	τ+ϵ	τ+ϵ	X
ejpam-4830	292	12	=	=	PUNCT
ejpam-4830	293	1	τd(t	τd(t	X
ejpam-4830	293	2	,	,	PUNCT
ejpam-4830	293	3	x+	x+	ADJ
ejpam-4830	293	4	ϵ	ϵ	X
ejpam-4830	293	5	,	,	PUNCT
ejpam-4830	293	6	j	j	PROPN
ejpam-4830	293	7	)	)	PUNCT
ejpam-4830	293	8	as	as	ADP
ejpam-4830	293	9	in	in	ADP
ejpam-4830	293	10	(	(	PUNCT
ejpam-4830	293	11	27	27	NUM
ejpam-4830	293	12	)	)	PUNCT
ejpam-4830	293	13	.	.	PUNCT
ejpam-4830	294	1	noting	note	VERB
ejpam-4830	294	2	that	that	SCONJ
ejpam-4830	294	3	τ+ϵ	τ+ϵ	PUNCT
ejpam-4830	294	4	→	→	SYM
ejpam-4830	294	5	0	0	NUM
ejpam-4830	294	6	as	as	ADP
ejpam-4830	294	7	ϵ	ϵ	PROPN
ejpam-4830	294	8	→	→	SYM
ejpam-4830	294	9	0	0	PUNCT
ejpam-4830	294	10	as	as	SCONJ
ejpam-4830	294	11	claimed	claim	VERB
ejpam-4830	294	12	in	in	ADP
ejpam-4830	294	13	(	(	PUNCT
ejpam-4830	294	14	29	29	NUM
ejpam-4830	294	15	)	)	PUNCT
ejpam-4830	294	16	,	,	PUNCT
ejpam-4830	294	17	by	by	ADP
ejpam-4830	294	18	(	(	PUNCT
ejpam-4830	294	19	30	30	NUM
ejpam-4830	294	20	)	)	PUNCT
ejpam-4830	294	21	we	we	PRON
ejpam-4830	294	22	have	have	VERB
ejpam-4830	294	23	∂gµc	∂gµc	NOUN
ejpam-4830	294	24	∂x	∂x	PROPN
ejpam-4830	294	25	(	(	PUNCT
ejpam-4830	294	26	t	t	PROPN
ejpam-4830	294	27	,	,	PUNCT
ejpam-4830	294	28	x	x	PROPN
ejpam-4830	294	29	,	,	PUNCT
ejpam-4830	294	30	j	j	PROPN
ejpam-4830	294	31	)	)	PUNCT
ejpam-4830	294	32	≥	≥	PROPN
ejpam-4830	295	1	lim	lim	PROPN
ejpam-4830	295	2	sup	sup	PROPN
ejpam-4830	295	3	ϵ	ϵ	PROPN
ejpam-4830	295	4	↘	↘	PROPN
ejpam-4830	295	5	0	0	PROPN
ejpam-4830	295	6	v	v	PROPN
ejpam-4830	295	7	(	(	PUNCT
ejpam-4830	295	8	t	t	PROPN
ejpam-4830	295	9	,	,	PUNCT
ejpam-4830	295	10	x+	x+	PROPN
ejpam-4830	295	11	ϵ	ϵ	X
ejpam-4830	295	12	,	,	PUNCT
ejpam-4830	295	13	j)−	j)−	PROPN
ejpam-4830	295	14	v	v	PROPN
ejpam-4830	295	15	(	(	PUNCT
ejpam-4830	295	16	t	t	PROPN
ejpam-4830	295	17	,	,	PUNCT
ejpam-4830	295	18	x	x	NOUN
ejpam-4830	295	19	,	,	PUNCT
ejpam-4830	295	20	j	j	PROPN
ejpam-4830	295	21	)	)	PUNCT
ejpam-4830	295	22	ϵ	ϵ	X
ejpam-4830	295	23	.	.	PUNCT
ejpam-4830	296	1	on	on	ADP
ejpam-4830	296	2	the	the	DET
ejpam-4830	296	3	other	other	ADJ
ejpam-4830	296	4	hand	hand	NOUN
ejpam-4830	296	5	,	,	PUNCT
ejpam-4830	296	6	since	since	SCONJ
ejpam-4830	296	7	(	(	PUNCT
ejpam-4830	296	8	t	t	PROPN
ejpam-4830	296	9	,	,	PUNCT
ejpam-4830	296	10	x	x	PROPN
ejpam-4830	296	11	,	,	PUNCT
ejpam-4830	296	12	j	j	NOUN
ejpam-4830	296	13	)	)	PUNCT
ejpam-4830	296	14	∈	∈	PROPN
ejpam-4830	296	15	∂c	∂c	PROPN
ejpam-4830	297	1	⊂	⊂	PROPN
ejpam-4830	297	2	d	d	X
ejpam-4830	297	3	,	,	PUNCT
ejpam-4830	297	4	we	we	PRON
ejpam-4830	297	5	have	have	VERB
ejpam-4830	297	6	lim	lim	PROPN
ejpam-4830	297	7	inf	inf	PROPN
ejpam-4830	298	1	ϵ	ϵ	PROPN
ejpam-4830	298	2	↘	↘	PROPN
ejpam-4830	298	3	0	0	PROPN
ejpam-4830	298	4	v	v	PROPN
ejpam-4830	298	5	(	(	PUNCT
ejpam-4830	298	6	t	t	PROPN
ejpam-4830	298	7	,	,	PUNCT
ejpam-4830	298	8	x+	x+	PROPN
ejpam-4830	298	9	ϵ	ϵ	X
ejpam-4830	298	10	,	,	PUNCT
ejpam-4830	298	11	j)−	j)−	PROPN
ejpam-4830	298	12	v	v	PROPN
ejpam-4830	298	13	(	(	PUNCT
ejpam-4830	298	14	t	t	PROPN
ejpam-4830	298	15	,	,	PUNCT
ejpam-4830	298	16	x	x	NOUN
ejpam-4830	298	17	,	,	PUNCT
ejpam-4830	298	18	j	j	PROPN
ejpam-4830	298	19	)	)	PUNCT
ejpam-4830	298	20	ϵ	ϵ	ADP
ejpam-4830	298	21	≥	≥	PROPN
ejpam-4830	298	22	lim	lim	PROPN
ejpam-4830	298	23	inf	inf	PROPN
ejpam-4830	298	24	ϵ	ϵ	PROPN
ejpam-4830	298	25	↘	↘	PROPN
ejpam-4830	298	26	0	0	PROPN
ejpam-4830	298	27	gµc(t	gµc(t	PROPN
ejpam-4830	298	28	,	,	PUNCT
ejpam-4830	298	29	x+	x+	PROPN
ejpam-4830	298	30	ϵ	ϵ	X
ejpam-4830	298	31	,	,	PUNCT
ejpam-4830	298	32	j)−gµc(t	j)−gµc(t	PROPN
ejpam-4830	298	33	,	,	PUNCT
ejpam-4830	298	34	x	x	PROPN
ejpam-4830	298	35	,	,	PUNCT
ejpam-4830	298	36	j	j	PROPN
ejpam-4830	298	37	)	)	PUNCT
ejpam-4830	298	38	ϵ	ϵ	NOUN
ejpam-4830	298	39	=	=	SYM
ejpam-4830	298	40	∂gµc	∂gµc	X
ejpam-4830	298	41	∂x	∂x	PROPN
ejpam-4830	298	42	(	(	PUNCT
ejpam-4830	298	43	t	t	PROPN
ejpam-4830	298	44	,	,	PUNCT
ejpam-4830	298	45	x	x	PROPN
ejpam-4830	298	46	,	,	PUNCT
ejpam-4830	298	47	j	j	PROPN
ejpam-4830	298	48	)	)	PUNCT
ejpam-4830	298	49	.	.	PUNCT
ejpam-4830	299	1	since	since	SCONJ
ejpam-4830	299	2	v	v	NOUN
ejpam-4830	299	3	=	=	SYM
ejpam-4830	299	4	gµc	gµc	NOUN
ejpam-4830	299	5	on	on	ADP
ejpam-4830	299	6	a	a	DET
ejpam-4830	299	7	closed	closed	ADJ
ejpam-4830	299	8	set	set	NOUN
ejpam-4830	299	9	d	d	NOUN
ejpam-4830	299	10	,	,	PUNCT
ejpam-4830	299	11	we	we	PRON
ejpam-4830	299	12	have	have	VERB
ejpam-4830	299	13	∂v	∂v	PROPN
ejpam-4830	299	14	∂x	∂x	PROPN
ejpam-4830	299	15	(	(	PUNCT
ejpam-4830	299	16	t	t	PROPN
ejpam-4830	299	17	,	,	PUNCT
ejpam-4830	299	18	x−	x−	PROPN
ejpam-4830	299	19	,	,	PUNCT
ejpam-4830	299	20	j	j	NOUN
ejpam-4830	299	21	)	)	PUNCT
ejpam-4830	299	22	=	=	SYM
ejpam-4830	299	23	∂gµc	∂gµc	X
ejpam-4830	299	24	∂x	∂x	PROPN
ejpam-4830	299	25	(	(	PUNCT
ejpam-4830	299	26	t	t	PROPN
ejpam-4830	299	27	,	,	PUNCT
ejpam-4830	299	28	x	x	PROPN
ejpam-4830	299	29	,	,	PUNCT
ejpam-4830	299	30	j	j	NOUN
ejpam-4830	299	31	)	)	PUNCT
ejpam-4830	300	1	=	=	PUNCT
ejpam-4830	300	2	∂v	∂v	PROPN
ejpam-4830	300	3	∂x	∂x	PROPN
ejpam-4830	300	4	(	(	PUNCT
ejpam-4830	300	5	t	t	PROPN
ejpam-4830	300	6	,	,	PUNCT
ejpam-4830	300	7	x−	x−	PROPN
ejpam-4830	300	8	,	,	PUNCT
ejpam-4830	300	9	j	j	PROPN
ejpam-4830	300	10	)	)	PUNCT
ejpam-4830	300	11	.	.	PUNCT
ejpam-4830	301	1	(	(	PUNCT
ejpam-4830	301	2	40	40	NUM
ejpam-4830	301	3	)	)	PUNCT
ejpam-4830	301	4	lemma	lemma	PROPN
ejpam-4830	301	5	8	8	NUM
ejpam-4830	301	6	.	.	PUNCT
ejpam-4830	302	1	we	we	PRON
ejpam-4830	302	2	have	have	VERB
ejpam-4830	302	3	{	{	PUNCT
ejpam-4830	302	4	(	(	PUNCT
ejpam-4830	302	5	t	t	PROPN
ejpam-4830	302	6	,	,	PUNCT
ejpam-4830	302	7	x	x	X
ejpam-4830	302	8	,	,	PUNCT
ejpam-4830	302	9	i	i	NOUN
ejpam-4830	302	10	)	)	PUNCT
ejpam-4830	302	11	∈	∈	PROPN
ejpam-4830	303	1	[	[	X
ejpam-4830	303	2	0	0	NUM
ejpam-4830	303	3	,	,	PUNCT
ejpam-4830	303	4	t	t	X
ejpam-4830	303	5	]	]	X
ejpam-4830	303	6	×	×	NOUN
ejpam-4830	303	7	(	(	PUNCT
ejpam-4830	303	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	303	9	:	:	PUNCT
ejpam-4830	303	10	lgµc(t	lgµc(t	PROPN
ejpam-4830	303	11	,	,	PUNCT
ejpam-4830	303	12	x	x	NOUN
ejpam-4830	303	13	,	,	PUNCT
ejpam-4830	303	14	i	i	PROPN
ejpam-4830	303	15	)	)	PUNCT
ejpam-4830	303	16	>	>	X
ejpam-4830	303	17	0	0	X
ejpam-4830	303	18	}	}	PUNCT
ejpam-4830	303	19	⊂	⊂	PROPN
ejpam-4830	303	20	c	c	X
ejpam-4830	303	21	where	where	SCONJ
ejpam-4830	303	22	c	c	NOUN
ejpam-4830	303	23	=	=	SYM
ejpam-4830	303	24	dc	dc	PROPN
ejpam-4830	303	25	is	be	AUX
ejpam-4830	303	26	the	the	DET
ejpam-4830	303	27	continuation	continuation	NOUN
ejpam-4830	303	28	set	set	NOUN
ejpam-4830	303	29	.	.	PUNCT
ejpam-4830	304	1	f.	f.	PROPN
ejpam-4830	304	2	sumalpong	sumalpong	PROPN
ejpam-4830	304	3	,	,	PUNCT
ejpam-4830	304	4	m.	m.	PROPN
ejpam-4830	304	5	frondoza	frondoza	PROPN
ejpam-4830	304	6	,	,	PUNCT
ejpam-4830	304	7	n.l	n.l	PROPN
ejpam-4830	304	8	.	.	PROPN
ejpam-4830	304	9	sayson	sayson	PROPN
ejpam-4830	304	10	/	/	SYM
ejpam-4830	304	11	eur	eur	PROPN
ejpam-4830	304	12	.	.	PUNCT
ejpam-4830	305	1	j.	j.	PROPN
ejpam-4830	305	2	pure	pure	PROPN
ejpam-4830	305	3	appl	appl	PROPN
ejpam-4830	305	4	.	.	PROPN
ejpam-4830	305	5	math	math	PROPN
ejpam-4830	305	6	,	,	PUNCT
ejpam-4830	305	7	16	16	NUM
ejpam-4830	305	8	(	(	PUNCT
ejpam-4830	305	9	3	3	NUM
ejpam-4830	305	10	)	)	PUNCT
ejpam-4830	305	11	(	(	PUNCT
ejpam-4830	305	12	2023	2023	NUM
ejpam-4830	305	13	)	)	PUNCT
ejpam-4830	305	14	,	,	PUNCT
ejpam-4830	305	15	1830	1830	NUM
ejpam-4830	305	16	-	-	SYM
ejpam-4830	305	17	1847	1847	NUM
ejpam-4830	305	18	1842	1842	NUM
ejpam-4830	305	19	proof	proof	NOUN
ejpam-4830	305	20	.	.	PUNCT
ejpam-4830	306	1	let	let	VERB
ejpam-4830	306	2	(	(	PUNCT
ejpam-4830	306	3	t	t	PROPN
ejpam-4830	306	4	,	,	PUNCT
ejpam-4830	306	5	x	x	X
ejpam-4830	306	6	,	,	PUNCT
ejpam-4830	306	7	i	i	NOUN
ejpam-4830	306	8	)	)	PUNCT
ejpam-4830	306	9	∈	∈	PROPN
ejpam-4830	307	1	[	[	X
ejpam-4830	307	2	0	0	NUM
ejpam-4830	307	3	,	,	PUNCT
ejpam-4830	307	4	t	t	X
ejpam-4830	307	5	]	]	X
ejpam-4830	307	6	×	×	NOUN
ejpam-4830	307	7	(	(	PUNCT
ejpam-4830	307	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	307	9	be	be	VERB
ejpam-4830	307	10	such	such	ADJ
ejpam-4830	307	11	that	that	PRON
ejpam-4830	307	12	lgµc(t	lgµc(t	PROPN
ejpam-4830	307	13	,	,	PUNCT
ejpam-4830	307	14	x	x	NOUN
ejpam-4830	307	15	,	,	PUNCT
ejpam-4830	307	16	i	i	PROPN
ejpam-4830	307	17	)	)	PUNCT
ejpam-4830	307	18	>	>	X
ejpam-4830	307	19	0	0	X
ejpam-4830	307	20	.	.	PUNCT
ejpam-4830	308	1	by	by	ADP
ejpam-4830	308	2	lemma	lemma	PROPN
ejpam-4830	308	3	1	1	NUM
ejpam-4830	308	4	in	in	ADP
ejpam-4830	308	5	[	[	X
ejpam-4830	308	6	2	2	X
ejpam-4830	308	7	]	]	PUNCT
ejpam-4830	308	8	we	we	PRON
ejpam-4830	308	9	have	have	VERB
ejpam-4830	308	10	e−rsgµc(t+	e−rsgµc(t+	PROPN
ejpam-4830	308	11	s	s	PROPN
ejpam-4830	308	12	,	,	PUNCT
ejpam-4830	308	13	xt+s	xt+s	PROPN
ejpam-4830	308	14	,	,	PUNCT
ejpam-4830	308	15	αt+s	αt+s	NUM
ejpam-4830	308	16	)	)	PUNCT
ejpam-4830	309	1	=	=	SYM
ejpam-4830	309	2	gµc(t	gµc(t	PROPN
ejpam-4830	309	3	,	,	PUNCT
ejpam-4830	309	4	x	x	NOUN
ejpam-4830	309	5	,	,	PUNCT
ejpam-4830	309	6	i	i	PROPN
ejpam-4830	309	7	)	)	PUNCT
ejpam-4830	310	1	+	+	CCONJ
ejpam-4830	310	2	∫	∫	PROPN
ejpam-4830	310	3	t+s	t+s	PROPN
ejpam-4830	310	4	t	t	PROPN
ejpam-4830	310	5	e−rulgµc(u	e−rulgµc(u	PROPN
ejpam-4830	310	6	,	,	PUNCT
ejpam-4830	310	7	xu	xu	PROPN
ejpam-4830	310	8	,	,	PUNCT
ejpam-4830	310	9	αu)du+ms	αu)du+ms	PROPN
ejpam-4830	310	10	,	,	PUNCT
ejpam-4830	310	11	(	(	PUNCT
ejpam-4830	310	12	41	41	NUM
ejpam-4830	310	13	)	)	PUNCT
ejpam-4830	310	14	where	where	SCONJ
ejpam-4830	310	15	ms	ms	PROPN
ejpam-4830	310	16	=	=	PROPN
ejpam-4830	310	17	∫	∫	PROPN
ejpam-4830	310	18	t+s	t+s	PROPN
ejpam-4830	310	19	t	t	PROPN
ejpam-4830	310	20	e−ruσ(αu)xu	e−ruσ(αu)xu	NOUN
ejpam-4830	310	21	∂gµc	∂gµc	PRON
ejpam-4830	310	22	∂x	∂x	PROPN
ejpam-4830	310	23	(	(	PUNCT
ejpam-4830	310	24	u	u	PROPN
ejpam-4830	310	25	,	,	PUNCT
ejpam-4830	310	26	xu	xu	PROPN
ejpam-4830	310	27	,	,	PUNCT
ejpam-4830	310	28	αu)dw	αu)dw	PRON
ejpam-4830	310	29	µc	µc	AUX
ejpam-4830	310	30	u	u	NOUN
ejpam-4830	310	31	defines	define	VERB
ejpam-4830	310	32	a	a	DET
ejpam-4830	310	33	continuous	continuous	ADJ
ejpam-4830	310	34	martingale	martingale	NOUN
ejpam-4830	310	35	for	for	ADP
ejpam-4830	310	36	s	s	X
ejpam-4830	310	37	∈	∈	PROPN
ejpam-4830	311	1	[	[	X
ejpam-4830	311	2	0	0	NUM
ejpam-4830	311	3	,	,	PUNCT
ejpam-4830	311	4	t−t	t−t	PROPN
ejpam-4830	311	5	]	]	PUNCT
ejpam-4830	311	6	with	with	ADP
ejpam-4830	311	7	t	t	PROPN
ejpam-4830	311	8	∈	∈	PROPN
ejpam-4830	312	1	[	[	X
ejpam-4830	312	2	0	0	NUM
ejpam-4830	312	3	,	,	PUNCT
ejpam-4830	312	4	t	t	NOUN
ejpam-4830	312	5	)	)	PUNCT
ejpam-4830	312	6	.	.	PUNCT
ejpam-4830	313	1	by	by	ADP
ejpam-4830	313	2	lemma	lemma	PROPN
ejpam-4830	313	3	(	(	PUNCT
ejpam-4830	313	4	1	1	NUM
ejpam-4830	313	5	)	)	PUNCT
ejpam-4830	313	6	,	,	PUNCT
ejpam-4830	313	7	lemma	lemma	PROPN
ejpam-4830	313	8	(	(	PUNCT
ejpam-4830	313	9	4	4	NUM
ejpam-4830	313	10	)	)	PUNCT
ejpam-4830	313	11	and	and	CCONJ
ejpam-4830	313	12	equation	equation	NOUN
ejpam-4830	313	13	(	(	PUNCT
ejpam-4830	313	14	37	37	NUM
ejpam-4830	313	15	)	)	PUNCT
ejpam-4830	313	16	,	,	PUNCT
ejpam-4830	313	17	the	the	DET
ejpam-4830	313	18	infinitesimal	infinitesimal	ADJ
ejpam-4830	313	19	generator	generator	NOUN
ejpam-4830	313	20	lgµc(t	lgµc(t	PROPN
ejpam-4830	313	21	,	,	PUNCT
ejpam-4830	313	22	x	x	PROPN
ejpam-4830	313	23	,	,	PUNCT
ejpam-4830	313	24	j	j	NOUN
ejpam-4830	313	25	)	)	PUNCT
ejpam-4830	313	26	is	be	AUX
ejpam-4830	313	27	continuous	continuous	ADJ
ejpam-4830	313	28	with	with	ADP
ejpam-4830	313	29	respect	respect	NOUN
ejpam-4830	313	30	to	to	ADP
ejpam-4830	313	31	(	(	PUNCT
ejpam-4830	313	32	t	t	PROPN
ejpam-4830	313	33	,	,	PUNCT
ejpam-4830	313	34	x	x	NOUN
ejpam-4830	313	35	)	)	PUNCT
ejpam-4830	313	36	∈	∈	PROPN
ejpam-4830	314	1	[	[	X
ejpam-4830	314	2	0	0	NUM
ejpam-4830	314	3	,	,	PUNCT
ejpam-4830	314	4	t	t	X
ejpam-4830	314	5	]	]	X
ejpam-4830	314	6	×	×	PROPN
ejpam-4830	314	7	(	(	PUNCT
ejpam-4830	314	8	0,∞	0,∞	NOUN
ejpam-4830	314	9	)	)	PUNCT
ejpam-4830	314	10	.	.	PUNCT
ejpam-4830	315	1	thus	thus	ADV
ejpam-4830	315	2	there	there	PRON
ejpam-4830	315	3	exists	exist	VERB
ejpam-4830	315	4	an	an	DET
ejpam-4830	315	5	open	open	ADJ
ejpam-4830	315	6	neighborhood	neighborhood	NOUN
ejpam-4830	315	7	u	u	NOUN
ejpam-4830	315	8	×	×	NOUN
ejpam-4830	315	9	v	v	ADP
ejpam-4830	315	10	⊂	⊂	PROPN
ejpam-4830	316	1	[	[	X
ejpam-4830	316	2	0	0	NUM
ejpam-4830	316	3	,	,	PUNCT
ejpam-4830	316	4	t	t	NOUN
ejpam-4830	316	5	)	)	PUNCT
ejpam-4830	316	6	×	×	NOUN
ejpam-4830	316	7	(	(	PUNCT
ejpam-4830	316	8	0,∞	0,∞	NOUN
ejpam-4830	316	9	)	)	PUNCT
ejpam-4830	316	10	of	of	ADP
ejpam-4830	316	11	(	(	PUNCT
ejpam-4830	316	12	t	t	PROPN
ejpam-4830	316	13	,	,	PUNCT
ejpam-4830	316	14	x	x	NOUN
ejpam-4830	316	15	)	)	PUNCT
ejpam-4830	316	16	such	such	ADJ
ejpam-4830	316	17	that	that	SCONJ
ejpam-4830	316	18	lgµc(s	lgµc(s	ADP
ejpam-4830	316	19	,	,	PUNCT
ejpam-4830	316	20	y	y	PROPN
ejpam-4830	316	21	,	,	PUNCT
ejpam-4830	316	22	j	j	PROPN
ejpam-4830	316	23	)	)	PUNCT
ejpam-4830	316	24	>	>	X
ejpam-4830	316	25	0	0	PUNCT
ejpam-4830	317	1	for	for	ADP
ejpam-4830	317	2	all	all	PRON
ejpam-4830	317	3	(	(	PUNCT
ejpam-4830	317	4	s	s	PROPN
ejpam-4830	317	5	,	,	PUNCT
ejpam-4830	317	6	y	y	NOUN
ejpam-4830	317	7	)	)	PUNCT
ejpam-4830	317	8	∈	∈	PROPN
ejpam-4830	317	9	u	u	NOUN
ejpam-4830	317	10	×	×	NOUN
ejpam-4830	317	11	v	v	NOUN
ejpam-4830	317	12	.	.	PUNCT
ejpam-4830	318	1	let	let	VERB
ejpam-4830	318	2	τu	τu	ADP
ejpam-4830	319	1	=	=	PUNCT
ejpam-4830	319	2	inf{τ	inf{τ	ADJ
ejpam-4830	319	3	:	:	PUNCT
ejpam-4830	319	4	(	(	PUNCT
ejpam-4830	319	5	t+	t+	X
ejpam-4830	319	6	τ	τ	X
ejpam-4830	319	7	,	,	PUNCT
ejpam-4830	319	8	xt+τ	xt+τ	PROPN
ejpam-4830	319	9	)	)	PUNCT
ejpam-4830	320	1	∈	∈	PROPN
ejpam-4830	321	1	u	u	NOUN
ejpam-4830	321	2	×	×	PROPN
ejpam-4830	321	3	v	v	NOUN
ejpam-4830	321	4	,	,	PUNCT
ejpam-4830	321	5	(	(	PUNCT
ejpam-4830	321	6	xt	xt	X
ejpam-4830	321	7	,	,	PUNCT
ejpam-4830	321	8	αt	αt	NOUN
ejpam-4830	321	9	)	)	PUNCT
ejpam-4830	321	10	=	=	SYM
ejpam-4830	322	1	(	(	PUNCT
ejpam-4830	322	2	x	x	X
ejpam-4830	322	3	,	,	PUNCT
ejpam-4830	322	4	i	i	NOUN
ejpam-4830	322	5	)	)	PUNCT
ejpam-4830	322	6	∈	∈	PROPN
ejpam-4830	322	7	v	v	ADP
ejpam-4830	322	8	×m	×m	NOUN
ejpam-4830	322	9	}	}	PUNCT
ejpam-4830	322	10	.	.	PUNCT
ejpam-4830	323	1	by	by	ADP
ejpam-4830	323	2	optional	optional	ADJ
ejpam-4830	323	3	sampling	sampling	NOUN
ejpam-4830	323	4	theorem	theorem	NOUN
ejpam-4830	323	5	,	,	PUNCT
ejpam-4830	323	6	the	the	DET
ejpam-4830	323	7	relation	relation	NOUN
ejpam-4830	323	8	(	(	PUNCT
ejpam-4830	323	9	41	41	NUM
ejpam-4830	323	10	)	)	PUNCT
ejpam-4830	323	11	with	with	ADP
ejpam-4830	323	12	s	s	NOUN
ejpam-4830	323	13	=	=	PUNCT
ejpam-4830	323	14	τu	τu	PART
ejpam-4830	323	15	shows	show	VERB
ejpam-4830	323	16	that	that	SCONJ
ejpam-4830	323	17	e	e	PROPN
ejpam-4830	323	18	[	[	PUNCT
ejpam-4830	323	19	e−rτugµc(t+	e−rτugµc(t+	X
ejpam-4830	323	20	τu	τu	ADP
ejpam-4830	323	21	,	,	PUNCT
ejpam-4830	323	22	xt+τu	xt+τu	PROPN
ejpam-4830	323	23	,	,	PUNCT
ejpam-4830	323	24	αt+τu	αt+τu	PROPN
ejpam-4830	323	25	)	)	PUNCT
ejpam-4830	323	26	∣∣∣ft	∣∣∣ft	PUNCT
ejpam-4830	323	27	]	]	PUNCT
ejpam-4830	324	1	=	=	SYM
ejpam-4830	324	2	gµc(t	gµc(t	PROPN
ejpam-4830	324	3	,	,	PUNCT
ejpam-4830	324	4	x	x	NOUN
ejpam-4830	324	5	,	,	PUNCT
ejpam-4830	324	6	i	i	NOUN
ejpam-4830	324	7	)	)	PUNCT
ejpam-4830	325	1	+	+	CCONJ
ejpam-4830	325	2	e	e	X
ejpam-4830	326	1	[	[	X
ejpam-4830	326	2	∫	∫	X
ejpam-4830	326	3	t+τu	t+τu	PROPN
ejpam-4830	326	4	t	t	PROPN
ejpam-4830	326	5	e−rulgµc(u	e−rulgµc(u	PROPN
ejpam-4830	326	6	,	,	PUNCT
ejpam-4830	326	7	xu	xu	PROPN
ejpam-4830	326	8	,	,	PUNCT
ejpam-4830	326	9	αu)du	αu)du	X
ejpam-4830	326	10	∣∣∣ft	∣∣∣ft	X
ejpam-4830	326	11	]	]	PUNCT
ejpam-4830	326	12	.	.	PUNCT
ejpam-4830	327	1	(	(	PUNCT
ejpam-4830	327	2	42	42	NUM
ejpam-4830	327	3	)	)	PUNCT
ejpam-4830	327	4	since	since	SCONJ
ejpam-4830	327	5	lgµc(u	lgµc(u	PROPN
ejpam-4830	327	6	,	,	PUNCT
ejpam-4830	327	7	xu	xu	PROPN
ejpam-4830	327	8	,	,	PUNCT
ejpam-4830	327	9	αu	αu	NOUN
ejpam-4830	327	10	)	)	PUNCT
ejpam-4830	327	11	>	>	X
ejpam-4830	327	12	0	0	PUNCT
ejpam-4830	328	1	for	for	ADP
ejpam-4830	328	2	u	u	PROPN
ejpam-4830	328	3	∈	∈	PROPN
ejpam-4830	328	4	(	(	PUNCT
ejpam-4830	328	5	t	t	PROPN
ejpam-4830	328	6	,	,	PUNCT
ejpam-4830	328	7	t+τu	t+τu	PROPN
ejpam-4830	328	8	)	)	PUNCT
ejpam-4830	328	9	,	,	PUNCT
ejpam-4830	328	10	the	the	DET
ejpam-4830	328	11	right	right	ADJ
ejpam-4830	328	12	hand	hand	NOUN
ejpam-4830	328	13	side	side	NOUN
ejpam-4830	328	14	of	of	ADP
ejpam-4830	328	15	equation	equation	NOUN
ejpam-4830	328	16	(	(	PUNCT
ejpam-4830	328	17	42	42	NUM
ejpam-4830	328	18	)	)	PUNCT
ejpam-4830	328	19	is	be	AUX
ejpam-4830	328	20	strictly	strictly	ADV
ejpam-4830	328	21	greater	great	ADJ
ejpam-4830	328	22	than	than	ADP
ejpam-4830	328	23	gµc(t	gµc(t	PROPN
ejpam-4830	328	24	,	,	PUNCT
ejpam-4830	328	25	x	x	NOUN
ejpam-4830	328	26	,	,	PUNCT
ejpam-4830	328	27	i	i	PROPN
ejpam-4830	328	28	)	)	PUNCT
ejpam-4830	328	29	,	,	PUNCT
ejpam-4830	328	30	while	while	SCONJ
ejpam-4830	328	31	from	from	ADP
ejpam-4830	328	32	equation	equation	NOUN
ejpam-4830	328	33	(	(	PUNCT
ejpam-4830	328	34	15	15	NUM
ejpam-4830	328	35	)	)	PUNCT
ejpam-4830	328	36	we	we	PRON
ejpam-4830	328	37	have	have	VERB
ejpam-4830	328	38	v	v	NUM
ejpam-4830	328	39	(	(	PUNCT
ejpam-4830	328	40	t	t	PROPN
ejpam-4830	328	41	,	,	PUNCT
ejpam-4830	328	42	x	x	X
ejpam-4830	328	43	,	,	PUNCT
ejpam-4830	328	44	i	i	PROPN
ejpam-4830	328	45	)	)	PUNCT
ejpam-4830	328	46	≥	≥	X
ejpam-4830	329	1	e	e	X
ejpam-4830	330	1	[	[	PUNCT
ejpam-4830	330	2	e−rτugµc(t+	e−rτugµc(t+	X
ejpam-4830	330	3	τu	τu	ADP
ejpam-4830	330	4	,	,	PUNCT
ejpam-4830	330	5	xt+τu	xt+τu	PROPN
ejpam-4830	330	6	,	,	PUNCT
ejpam-4830	330	7	αt+τu	αt+τu	PROPN
ejpam-4830	330	8	)	)	PUNCT
ejpam-4830	330	9	|	|	ADV
ejpam-4830	330	10	ft	ft	X
ejpam-4830	330	11	]	]	PUNCT
ejpam-4830	330	12	showing	show	VERB
ejpam-4830	330	13	that	that	PRON
ejpam-4830	330	14	v	v	NOUN
ejpam-4830	330	15	(	(	PUNCT
ejpam-4830	330	16	t	t	PROPN
ejpam-4830	330	17	,	,	PUNCT
ejpam-4830	330	18	x	x	X
ejpam-4830	330	19	,	,	PUNCT
ejpam-4830	330	20	i	i	PROPN
ejpam-4830	330	21	)	)	PUNCT
ejpam-4830	330	22	>	>	X
ejpam-4830	331	1	gµc(t	gµc(t	PROPN
ejpam-4830	331	2	,	,	PUNCT
ejpam-4830	331	3	x	x	NOUN
ejpam-4830	331	4	,	,	PUNCT
ejpam-4830	331	5	i	i	PROPN
ejpam-4830	331	6	)	)	PUNCT
ejpam-4830	331	7	,	,	PUNCT
ejpam-4830	331	8	which	which	PRON
ejpam-4830	331	9	implies	imply	VERB
ejpam-4830	331	10	that	that	SCONJ
ejpam-4830	331	11	(	(	PUNCT
ejpam-4830	331	12	t	t	PROPN
ejpam-4830	331	13	,	,	PUNCT
ejpam-4830	331	14	x	x	X
ejpam-4830	331	15	,	,	PUNCT
ejpam-4830	331	16	i	i	NOUN
ejpam-4830	331	17	)	)	PUNCT
ejpam-4830	331	18	∈	∈	PROPN
ejpam-4830	331	19	c.	c.	NOUN
ejpam-4830	331	20	this	this	PRON
ejpam-4830	331	21	completes	complete	VERB
ejpam-4830	331	22	our	our	PRON
ejpam-4830	331	23	proof	proof	NOUN
ejpam-4830	331	24	.	.	PUNCT
ejpam-4830	332	1	next	next	ADV
ejpam-4830	332	2	,	,	PUNCT
ejpam-4830	332	3	we	we	PRON
ejpam-4830	332	4	define	define	VERB
ejpam-4830	332	5	the	the	DET
ejpam-4830	332	6	boundary	boundary	ADJ
ejpam-4830	332	7	function	function	NOUN
ejpam-4830	332	8	bd(t	bd(t	PROPN
ejpam-4830	332	9	,	,	PUNCT
ejpam-4830	332	10	j	j	NOUN
ejpam-4830	332	11	)	)	PUNCT
ejpam-4830	332	12	via	via	ADP
ejpam-4830	332	13	the	the	DET
ejpam-4830	332	14	following	following	NOUN
ejpam-4830	332	15	:	:	PUNCT
ejpam-4830	332	16	for	for	ADP
ejpam-4830	332	17	any	any	DET
ejpam-4830	332	18	stopping	stopping	NOUN
ejpam-4830	332	19	time	time	NOUN
ejpam-4830	332	20	τ	τ	X
ejpam-4830	332	21	∈	∈	PROPN
ejpam-4830	333	1	[	[	X
ejpam-4830	333	2	0	0	NUM
ejpam-4830	333	3	,	,	PUNCT
ejpam-4830	333	4	t	t	PROPN
ejpam-4830	333	5	−	−	PROPN
ejpam-4830	333	6	t	t	PROPN
ejpam-4830	333	7	]	]	PUNCT
ejpam-4830	333	8	,	,	PUNCT
ejpam-4830	333	9	it	it	PRON
ejpam-4830	333	10	can	can	AUX
ejpam-4830	333	11	be	be	AUX
ejpam-4830	333	12	verified	verify	VERB
ejpam-4830	333	13	from	from	ADP
ejpam-4830	333	14	equations	equation	NOUN
ejpam-4830	333	15	(	(	PUNCT
ejpam-4830	333	16	37	37	NUM
ejpam-4830	333	17	)	)	PUNCT
ejpam-4830	333	18	and	and	CCONJ
ejpam-4830	333	19	(	(	PUNCT
ejpam-4830	333	20	42	42	NUM
ejpam-4830	333	21	)	)	PUNCT
ejpam-4830	333	22	that	that	SCONJ
ejpam-4830	333	23	there	there	PRON
ejpam-4830	333	24	is	be	VERB
ejpam-4830	333	25	a	a	DET
ejpam-4830	333	26	continuous	continuous	ADJ
ejpam-4830	333	27	function	function	NOUN
ejpam-4830	333	28	h	h	NOUN
ejpam-4830	333	29	:	:	PUNCT
ejpam-4830	334	1	[	[	X
ejpam-4830	334	2	0	0	NUM
ejpam-4830	334	3	,	,	PUNCT
ejpam-4830	334	4	t	t	X
ejpam-4830	334	5	]	]	PUNCT
ejpam-4830	334	6	×m	×m	NOUN
ejpam-4830	334	7	→	→	SYM
ejpam-4830	334	8	r	r	NOUN
ejpam-4830	334	9	such	such	ADJ
ejpam-4830	334	10	that	that	SCONJ
ejpam-4830	334	11	the	the	DET
ejpam-4830	334	12	infinitesimal	infinitesimal	ADJ
ejpam-4830	334	13	generator	generator	NOUN
ejpam-4830	334	14	(	(	PUNCT
ejpam-4830	334	15	37	37	NUM
ejpam-4830	334	16	)	)	PUNCT
ejpam-4830	334	17	satisfies	satisfy	VERB
ejpam-4830	334	18	lgµc(t	lgµc(t	PROPN
ejpam-4830	334	19	,	,	PUNCT
ejpam-4830	334	20	h(t	h(t	PROPN
ejpam-4830	334	21	,	,	PUNCT
ejpam-4830	334	22	j	j	PROPN
ejpam-4830	334	23	)	)	PUNCT
ejpam-4830	334	24	,	,	PUNCT
ejpam-4830	334	25	j	j	NOUN
ejpam-4830	334	26	)	)	PUNCT
ejpam-4830	334	27	=	=	SYM
ejpam-4830	334	28	0	0	X
ejpam-4830	334	29	.	.	PUNCT
ejpam-4830	335	1	(	(	PUNCT
ejpam-4830	335	2	43	43	NUM
ejpam-4830	335	3	)	)	PUNCT
ejpam-4830	335	4	since	since	SCONJ
ejpam-4830	335	5	µc	µc	INTJ
ejpam-4830	335	6	>	>	X
ejpam-4830	335	7	r	r	NOUN
ejpam-4830	335	8	,	,	PUNCT
ejpam-4830	335	9	we	we	PRON
ejpam-4830	335	10	see	see	VERB
ejpam-4830	335	11	that	that	DET
ejpam-4830	335	12	lgµc(t	lgµc(t	PROPN
ejpam-4830	335	13	,	,	PUNCT
ejpam-4830	335	14	h(t	h(t	PROPN
ejpam-4830	335	15	,	,	PUNCT
ejpam-4830	335	16	j	j	PROPN
ejpam-4830	335	17	)	)	PUNCT
ejpam-4830	335	18	,	,	PUNCT
ejpam-4830	335	19	j	j	PROPN
ejpam-4830	335	20	)	)	PUNCT
ejpam-4830	335	21	>	>	X
ejpam-4830	335	22	0	0	PUNCT
ejpam-4830	336	1	for	for	ADP
ejpam-4830	336	2	x	x	X
ejpam-4830	336	3	>	>	X
ejpam-4830	336	4	h(t	h(t	PROPN
ejpam-4830	336	5	,	,	PUNCT
ejpam-4830	336	6	j	j	PROPN
ejpam-4830	336	7	)	)	PUNCT
ejpam-4830	336	8	and	and	CCONJ
ejpam-4830	336	9	lgµc(t	lgµc(t	PROPN
ejpam-4830	336	10	,	,	PUNCT
ejpam-4830	336	11	h(t	h(t	PROPN
ejpam-4830	336	12	,	,	PUNCT
ejpam-4830	336	13	j	j	PROPN
ejpam-4830	336	14	)	)	PUNCT
ejpam-4830	336	15	,	,	PUNCT
ejpam-4830	336	16	j	j	PROPN
ejpam-4830	336	17	)	)	PUNCT
ejpam-4830	336	18	<	<	X
ejpam-4830	336	19	0	0	PUNCT
ejpam-4830	336	20	for	for	ADP
ejpam-4830	336	21	x	x	X
ejpam-4830	336	22	<	<	X
ejpam-4830	336	23	h(t	h(t	PROPN
ejpam-4830	336	24	,	,	PUNCT
ejpam-4830	336	25	j	j	PROPN
ejpam-4830	336	26	)	)	PUNCT
ejpam-4830	336	27	when	when	SCONJ
ejpam-4830	336	28	t	t	PROPN
ejpam-4830	336	29	∈	∈	PROPN
ejpam-4830	337	1	[	[	X
ejpam-4830	337	2	0	0	NUM
ejpam-4830	337	3	,	,	PUNCT
ejpam-4830	337	4	t	t	NOUN
ejpam-4830	337	5	]	]	PUNCT
ejpam-4830	337	6	and	and	CCONJ
ejpam-4830	337	7	j	j	PROPN
ejpam-4830	337	8	∈	∈	PROPN
ejpam-4830	337	9	m	m	VERB
ejpam-4830	337	10	are	be	AUX
ejpam-4830	337	11	given	give	VERB
ejpam-4830	337	12	and	and	CCONJ
ejpam-4830	337	13	fixed	fix	VERB
ejpam-4830	337	14	.	.	PUNCT
ejpam-4830	338	1	in	in	ADP
ejpam-4830	338	2	view	view	NOUN
ejpam-4830	338	3	of	of	ADP
ejpam-4830	338	4	equation	equation	NOUN
ejpam-4830	338	5	(	(	PUNCT
ejpam-4830	338	6	42	42	NUM
ejpam-4830	338	7	)	)	PUNCT
ejpam-4830	338	8	,	,	PUNCT
ejpam-4830	338	9	this	this	PRON
ejpam-4830	338	10	implies	imply	VERB
ejpam-4830	338	11	that	that	SCONJ
ejpam-4830	338	12	for	for	ADP
ejpam-4830	338	13	any	any	DET
ejpam-4830	338	14	stopping	stopping	NOUN
ejpam-4830	338	15	time	time	NOUN
ejpam-4830	338	16	τ	τ	X
ejpam-4830	338	17	∈	∈	PROPN
ejpam-4830	339	1	[	[	X
ejpam-4830	339	2	0	0	NUM
ejpam-4830	339	3	,	,	PUNCT
ejpam-4830	339	4	t−t	t−t	PROPN
ejpam-4830	339	5	]	]	PUNCT
ejpam-4830	339	6	,	,	PUNCT
ejpam-4830	339	7	there	there	PRON
ejpam-4830	339	8	is	be	VERB
ejpam-4830	339	9	no	no	DET
ejpam-4830	339	10	point	point	NOUN
ejpam-4830	339	11	(	(	PUNCT
ejpam-4830	339	12	t	t	PROPN
ejpam-4830	339	13	,	,	PUNCT
ejpam-4830	339	14	x	x	NOUN
ejpam-4830	339	15	)	)	PUNCT
ejpam-4830	339	16	∈	∈	PROPN
ejpam-4830	340	1	[	[	X
ejpam-4830	340	2	0	0	NUM
ejpam-4830	340	3	,	,	PUNCT
ejpam-4830	340	4	t	t	NOUN
ejpam-4830	340	5	]	]	PUNCT
ejpam-4830	340	6	×(0,∞	×(0,∞	X
ejpam-4830	340	7	)	)	PUNCT
ejpam-4830	340	8	with	with	ADP
ejpam-4830	340	9	x	x	X
ejpam-4830	340	10	>	>	X
ejpam-4830	340	11	h(t	h(t	PROPN
ejpam-4830	340	12	,	,	PUNCT
ejpam-4830	340	13	j	j	NOUN
ejpam-4830	340	14	)	)	PUNCT
ejpam-4830	340	15	is	be	AUX
ejpam-4830	340	16	a	a	DET
ejpam-4830	340	17	stopping	stopping	NOUN
ejpam-4830	340	18	point	point	NOUN
ejpam-4830	340	19	.	.	PUNCT
ejpam-4830	341	1	from	from	ADP
ejpam-4830	341	2	here	here	ADV
ejpam-4830	341	3	,	,	PUNCT
ejpam-4830	341	4	we	we	PRON
ejpam-4830	341	5	define	define	VERB
ejpam-4830	341	6	the	the	DET
ejpam-4830	341	7	optimal	optimal	ADJ
ejpam-4830	341	8	stopping	stopping	NOUN
ejpam-4830	341	9	boundary	boundary	ADJ
ejpam-4830	341	10	as	as	SCONJ
ejpam-4830	341	11	follows	follow	VERB
ejpam-4830	341	12	:	:	PUNCT
ejpam-4830	341	13	bd(t	bd(t	PROPN
ejpam-4830	341	14	,	,	PUNCT
ejpam-4830	341	15	j	j	NOUN
ejpam-4830	341	16	)	)	PUNCT
ejpam-4830	341	17	:	:	PUNCT
ejpam-4830	342	1	=	=	SYM
ejpam-4830	342	2	sup	sup	INTJ
ejpam-4830	342	3	{	{	PUNCT
ejpam-4830	342	4	x	x	SYM
ejpam-4830	342	5	∈	∈	PROPN
ejpam-4830	342	6	(	(	PUNCT
ejpam-4830	342	7	0,∞	0,∞	NOUN
ejpam-4830	342	8	)	)	PUNCT
ejpam-4830	342	9	:	:	PUNCT
ejpam-4830	342	10	(	(	PUNCT
ejpam-4830	342	11	t	t	PROPN
ejpam-4830	342	12	,	,	PUNCT
ejpam-4830	342	13	x	x	PROPN
ejpam-4830	342	14	,	,	PUNCT
ejpam-4830	342	15	j	j	NOUN
ejpam-4830	342	16	)	)	PUNCT
ejpam-4830	342	17	∈	∈	PROPN
ejpam-4830	342	18	d	d	NOUN
ejpam-4830	342	19	}	}	PUNCT
ejpam-4830	342	20	.	.	PUNCT
ejpam-4830	343	1	(	(	PUNCT
ejpam-4830	343	2	44	44	NUM
ejpam-4830	343	3	)	)	PUNCT
ejpam-4830	343	4	f.	f.	PROPN
ejpam-4830	343	5	sumalpong	sumalpong	PROPN
ejpam-4830	343	6	,	,	PUNCT
ejpam-4830	343	7	m.	m.	PROPN
ejpam-4830	343	8	frondoza	frondoza	PROPN
ejpam-4830	343	9	,	,	PUNCT
ejpam-4830	343	10	n.l	n.l	PROPN
ejpam-4830	343	11	.	.	PROPN
ejpam-4830	343	12	sayson	sayson	PROPN
ejpam-4830	343	13	/	/	SYM
ejpam-4830	343	14	eur	eur	PROPN
ejpam-4830	343	15	.	.	PUNCT
ejpam-4830	344	1	j.	j.	PROPN
ejpam-4830	344	2	pure	pure	PROPN
ejpam-4830	344	3	appl	appl	PROPN
ejpam-4830	344	4	.	.	PROPN
ejpam-4830	344	5	math	math	PROPN
ejpam-4830	344	6	,	,	PUNCT
ejpam-4830	344	7	16	16	NUM
ejpam-4830	344	8	(	(	PUNCT
ejpam-4830	344	9	3	3	NUM
ejpam-4830	344	10	)	)	PUNCT
ejpam-4830	344	11	(	(	PUNCT
ejpam-4830	344	12	2023	2023	NUM
ejpam-4830	344	13	)	)	PUNCT
ejpam-4830	344	14	,	,	PUNCT
ejpam-4830	344	15	1830	1830	NUM
ejpam-4830	344	16	-	-	SYM
ejpam-4830	344	17	1847	1847	NUM
ejpam-4830	344	18	1843	1843	NUM
ejpam-4830	344	19	now	now	ADV
ejpam-4830	344	20	,	,	PUNCT
ejpam-4830	344	21	we	we	PRON
ejpam-4830	344	22	characterize	characterize	VERB
ejpam-4830	344	23	the	the	DET
ejpam-4830	344	24	stopping	stopping	NOUN
ejpam-4830	344	25	set	set	NOUN
ejpam-4830	344	26	defined	define	VERB
ejpam-4830	344	27	in	in	ADP
ejpam-4830	344	28	(	(	PUNCT
ejpam-4830	344	29	24	24	NUM
ejpam-4830	344	30	)	)	PUNCT
ejpam-4830	344	31	in	in	ADP
ejpam-4830	344	32	terms	term	NOUN
ejpam-4830	344	33	of	of	ADP
ejpam-4830	344	34	the	the	DET
ejpam-4830	344	35	boundary	boundary	ADJ
ejpam-4830	344	36	function	function	NOUN
ejpam-4830	344	37	bd(t	bd(t	PROPN
ejpam-4830	344	38	,	,	PUNCT
ejpam-4830	344	39	j	j	NOUN
ejpam-4830	344	40	)	)	PUNCT
ejpam-4830	344	41	.	.	PUNCT
ejpam-4830	345	1	proposition	proposition	NOUN
ejpam-4830	345	2	2	2	NUM
ejpam-4830	345	3	.	.	X
ejpam-4830	346	1	for	for	ADP
ejpam-4830	346	2	any	any	DET
ejpam-4830	346	3	(	(	PUNCT
ejpam-4830	346	4	t	t	PROPN
ejpam-4830	346	5	,	,	PUNCT
ejpam-4830	346	6	x	x	NOUN
ejpam-4830	346	7	,	,	PUNCT
ejpam-4830	346	8	j	j	NOUN
ejpam-4830	346	9	)	)	PUNCT
ejpam-4830	346	10	∈	∈	PROPN
ejpam-4830	347	1	[	[	X
ejpam-4830	347	2	0	0	NUM
ejpam-4830	347	3	,	,	PUNCT
ejpam-4830	347	4	t	t	X
ejpam-4830	347	5	]	]	X
ejpam-4830	347	6	×	×	NOUN
ejpam-4830	347	7	(	(	PUNCT
ejpam-4830	347	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	347	9	such	such	ADJ
ejpam-4830	347	10	that	that	PRON
ejpam-4830	347	11	(	(	PUNCT
ejpam-4830	347	12	t	t	PROPN
ejpam-4830	347	13	,	,	PUNCT
ejpam-4830	347	14	x	x	PROPN
ejpam-4830	347	15	,	,	PUNCT
ejpam-4830	347	16	j	j	NOUN
ejpam-4830	347	17	)	)	PUNCT
ejpam-4830	347	18	∈	∈	PROPN
ejpam-4830	348	1	d	d	X
ejpam-4830	348	2	we	we	PRON
ejpam-4830	348	3	have	have	VERB
ejpam-4830	348	4	{	{	PUNCT
ejpam-4830	348	5	t	t	PROPN
ejpam-4830	348	6	}	}	PUNCT
ejpam-4830	348	7	×	×	NOUN
ejpam-4830	348	8	(	(	PUNCT
ejpam-4830	348	9	0	0	NUM
ejpam-4830	348	10	,	,	PUNCT
ejpam-4830	348	11	x]×	x]×	PROPN
ejpam-4830	348	12	{	{	PUNCT
ejpam-4830	348	13	j	j	PROPN
ejpam-4830	348	14	}	}	PUNCT
ejpam-4830	348	15	⊂	⊂	PROPN
ejpam-4830	349	1	d	d	X
ejpam-4830	349	2	(	(	PUNCT
ejpam-4830	349	3	45	45	NUM
ejpam-4830	349	4	)	)	PUNCT
ejpam-4830	349	5	and	and	CCONJ
ejpam-4830	349	6	d	d	NOUN
ejpam-4830	349	7	=	=	SYM
ejpam-4830	349	8	{	{	PUNCT
ejpam-4830	349	9	(	(	PUNCT
ejpam-4830	349	10	t	t	PROPN
ejpam-4830	349	11	,	,	PUNCT
ejpam-4830	349	12	x	x	PROPN
ejpam-4830	349	13	,	,	PUNCT
ejpam-4830	349	14	j	j	NOUN
ejpam-4830	349	15	)	)	PUNCT
ejpam-4830	349	16	∈	∈	PROPN
ejpam-4830	350	1	[	[	X
ejpam-4830	350	2	0	0	NUM
ejpam-4830	350	3	,	,	PUNCT
ejpam-4830	350	4	t	t	X
ejpam-4830	350	5	]	]	X
ejpam-4830	350	6	×	×	NOUN
ejpam-4830	350	7	(	(	PUNCT
ejpam-4830	350	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	350	9	:	:	PUNCT
ejpam-4830	350	10	x	x	SYM
ejpam-4830	350	11	≤	≤	NUM
ejpam-4830	350	12	bd(t	bd(t	NOUN
ejpam-4830	350	13	,	,	PUNCT
ejpam-4830	350	14	j	j	NOUN
ejpam-4830	350	15	)	)	PUNCT
ejpam-4830	350	16	}	}	PUNCT
ejpam-4830	350	17	.	.	PUNCT
ejpam-4830	351	1	(	(	PUNCT
ejpam-4830	351	2	46	46	X
ejpam-4830	351	3	)	)	PUNCT
ejpam-4830	351	4	proof	proof	NOUN
ejpam-4830	351	5	.	.	PUNCT
ejpam-4830	352	1	let	let	VERB
ejpam-4830	352	2	(	(	PUNCT
ejpam-4830	352	3	t	t	PROPN
ejpam-4830	352	4	,	,	PUNCT
ejpam-4830	352	5	y	y	PROPN
ejpam-4830	352	6	,	,	PUNCT
ejpam-4830	352	7	j	j	PROPN
ejpam-4830	352	8	)	)	PUNCT
ejpam-4830	352	9	∈	∈	PROPN
ejpam-4830	352	10	{	{	PUNCT
ejpam-4830	352	11	t	t	PROPN
ejpam-4830	352	12	}	}	PUNCT
ejpam-4830	352	13	×	×	NOUN
ejpam-4830	352	14	(	(	PUNCT
ejpam-4830	352	15	0	0	NUM
ejpam-4830	352	16	,	,	PUNCT
ejpam-4830	352	17	x]×	x]×	PROPN
ejpam-4830	352	18	{	{	PUNCT
ejpam-4830	352	19	j	j	PROPN
ejpam-4830	352	20	}	}	PUNCT
ejpam-4830	352	21	.	.	PUNCT
ejpam-4830	353	1	since	since	SCONJ
ejpam-4830	353	2	(	(	PUNCT
ejpam-4830	353	3	t	t	PROPN
ejpam-4830	353	4	,	,	PUNCT
ejpam-4830	353	5	x	x	PROPN
ejpam-4830	353	6	,	,	PUNCT
ejpam-4830	353	7	j	j	NOUN
ejpam-4830	353	8	)	)	PUNCT
ejpam-4830	353	9	∈	∈	PROPN
ejpam-4830	353	10	d	d	NOUN
ejpam-4830	353	11	and	and	CCONJ
ejpam-4830	353	12	v	v	PROPN
ejpam-4830	353	13	(	(	PUNCT
ejpam-4830	353	14	t	t	PROPN
ejpam-4830	353	15	,	,	PUNCT
ejpam-4830	353	16	x	x	PROPN
ejpam-4830	353	17	,	,	PUNCT
ejpam-4830	353	18	j	j	PROPN
ejpam-4830	353	19	)	)	PUNCT
ejpam-4830	353	20	≥	≥	PROPN
ejpam-4830	354	1	gµc(t	gµc(t	NOUN
ejpam-4830	354	2	,	,	PUNCT
ejpam-4830	354	3	x	x	NOUN
ejpam-4830	354	4	,	,	PUNCT
ejpam-4830	354	5	j	j	NOUN
ejpam-4830	354	6	)	)	PUNCT
ejpam-4830	354	7	for	for	ADP
ejpam-4830	354	8	all	all	DET
ejpam-4830	354	9	x	x	SYM
ejpam-4830	354	10	∈	∈	PROPN
ejpam-4830	354	11	(	(	PUNCT
ejpam-4830	354	12	0,∞	0,∞	NOUN
ejpam-4830	354	13	)	)	PUNCT
ejpam-4830	354	14	,	,	PUNCT
ejpam-4830	354	15	we	we	PRON
ejpam-4830	354	16	have	have	VERB
ejpam-4830	354	17	v	v	NUM
ejpam-4830	354	18	(	(	PUNCT
ejpam-4830	354	19	t	t	PROPN
ejpam-4830	354	20	,	,	PUNCT
ejpam-4830	354	21	x	x	X
ejpam-4830	354	22	,	,	PUNCT
ejpam-4830	354	23	j)−	j)−	PROPN
ejpam-4830	354	24	v	v	PROPN
ejpam-4830	354	25	(	(	PUNCT
ejpam-4830	354	26	t	t	PROPN
ejpam-4830	354	27	,	,	PUNCT
ejpam-4830	354	28	y	y	PROPN
ejpam-4830	354	29	,	,	PUNCT
ejpam-4830	354	30	j	j	PROPN
ejpam-4830	354	31	)	)	PUNCT
ejpam-4830	354	32	x−	x−	PROPN
ejpam-4830	355	1	y	y	PROPN
ejpam-4830	355	2	=	=	SYM
ejpam-4830	355	3	gµc(t	gµc(t	PROPN
ejpam-4830	355	4	,	,	PUNCT
ejpam-4830	355	5	x	x	NOUN
ejpam-4830	355	6	,	,	PUNCT
ejpam-4830	355	7	j)−	j)−	PROPN
ejpam-4830	355	8	v	v	PROPN
ejpam-4830	355	9	(	(	PUNCT
ejpam-4830	355	10	t	t	PROPN
ejpam-4830	355	11	,	,	PUNCT
ejpam-4830	355	12	y	y	PROPN
ejpam-4830	355	13	,	,	PUNCT
ejpam-4830	355	14	j	j	PROPN
ejpam-4830	355	15	)	)	PUNCT
ejpam-4830	355	16	x−	x−	PROPN
ejpam-4830	356	1	y	y	PROPN
ejpam-4830	356	2	≤	≤	PROPN
ejpam-4830	356	3	gµc(t	gµc(t	PROPN
ejpam-4830	356	4	,	,	PUNCT
ejpam-4830	356	5	x	x	NOUN
ejpam-4830	356	6	,	,	PUNCT
ejpam-4830	356	7	j)−gµc(t	j)−gµc(t	PROPN
ejpam-4830	356	8	,	,	PUNCT
ejpam-4830	356	9	y	y	PROPN
ejpam-4830	356	10	,	,	PUNCT
ejpam-4830	356	11	j	j	PROPN
ejpam-4830	356	12	)	)	PUNCT
ejpam-4830	356	13	x−	x−	PROPN
ejpam-4830	356	14	y	y	PROPN
ejpam-4830	356	15	.	.	PUNCT
ejpam-4830	357	1	taking	take	VERB
ejpam-4830	357	2	the	the	DET
ejpam-4830	357	3	limit	limit	NOUN
ejpam-4830	357	4	on	on	ADP
ejpam-4830	357	5	both	both	DET
ejpam-4830	357	6	sides	side	NOUN
ejpam-4830	357	7	as	as	ADP
ejpam-4830	357	8	x−	x−	PROPN
ejpam-4830	357	9	y	y	PROPN
ejpam-4830	357	10	→	→	SYM
ejpam-4830	357	11	0	0	NUM
ejpam-4830	357	12	and	and	CCONJ
ejpam-4830	357	13	by	by	ADP
ejpam-4830	357	14	lemma	lemma	PROPN
ejpam-4830	357	15	(	(	PUNCT
ejpam-4830	357	16	3	3	NUM
ejpam-4830	357	17	)	)	PUNCT
ejpam-4830	357	18	,	,	PUNCT
ejpam-4830	357	19	we	we	PRON
ejpam-4830	357	20	have	have	VERB
ejpam-4830	357	21	(	(	PUNCT
ejpam-4830	357	22	t	t	PROPN
ejpam-4830	357	23	,	,	PUNCT
ejpam-4830	357	24	y	y	PROPN
ejpam-4830	357	25	,	,	PUNCT
ejpam-4830	357	26	j	j	PROPN
ejpam-4830	357	27	)	)	PUNCT
ejpam-4830	357	28	∈	∈	PROPN
ejpam-4830	357	29	d	d	NOUN
ejpam-4830	357	30	and	and	CCONJ
ejpam-4830	357	31	conclude	conclude	VERB
ejpam-4830	357	32	(	(	PUNCT
ejpam-4830	357	33	45	45	NUM
ejpam-4830	357	34	)	)	PUNCT
ejpam-4830	357	35	.	.	PUNCT
ejpam-4830	358	1	from	from	ADP
ejpam-4830	358	2	the	the	DET
ejpam-4830	358	3	definition	definition	NOUN
ejpam-4830	358	4	of	of	ADP
ejpam-4830	358	5	the	the	DET
ejpam-4830	358	6	boundary	boundary	ADJ
ejpam-4830	358	7	function	function	NOUN
ejpam-4830	358	8	in	in	ADP
ejpam-4830	358	9	(	(	PUNCT
ejpam-4830	358	10	44	44	NUM
ejpam-4830	358	11	)	)	PUNCT
ejpam-4830	358	12	,	,	PUNCT
ejpam-4830	358	13	we	we	PRON
ejpam-4830	358	14	have	have	VERB
ejpam-4830	358	15	the	the	DET
ejpam-4830	358	16	following	following	ADJ
ejpam-4830	358	17	equivalence	equivalence	NOUN
ejpam-4830	358	18	(	(	PUNCT
ejpam-4830	358	19	t	t	PROPN
ejpam-4830	358	20	,	,	PUNCT
ejpam-4830	358	21	x	x	PROPN
ejpam-4830	358	22	,	,	PUNCT
ejpam-4830	358	23	j	j	NOUN
ejpam-4830	358	24	)	)	PUNCT
ejpam-4830	358	25	∈	∈	PROPN
ejpam-4830	359	1	d	d	X
ejpam-4830	359	2	⇐	⇐	ADJ
ejpam-4830	359	3	⇒	⇒	PROPN
ejpam-4830	359	4	{	{	PUNCT
ejpam-4830	359	5	t	t	PROPN
ejpam-4830	359	6	}	}	PUNCT
ejpam-4830	359	7	×	×	NOUN
ejpam-4830	359	8	(	(	PUNCT
ejpam-4830	359	9	0	0	NUM
ejpam-4830	359	10	,	,	PUNCT
ejpam-4830	359	11	x]×	x]×	PROPN
ejpam-4830	359	12	{	{	PUNCT
ejpam-4830	359	13	j	j	PROPN
ejpam-4830	359	14	}	}	PUNCT
ejpam-4830	359	15	⊂	⊂	PROPN
ejpam-4830	360	1	d	d	X
ejpam-4830	360	2	⇐	⇐	ADJ
ejpam-4830	360	3	⇒	⇒	PROPN
ejpam-4830	360	4	x	x	SYM
ejpam-4830	360	5	≤	≤	X
ejpam-4830	360	6	bd(t	bd(t	NOUN
ejpam-4830	360	7	,	,	PUNCT
ejpam-4830	360	8	j	j	PROPN
ejpam-4830	360	9	)	)	PUNCT
ejpam-4830	360	10	.	.	PUNCT
ejpam-4830	361	1	lemma	lemma	PROPN
ejpam-4830	361	2	9	9	NUM
ejpam-4830	361	3	.	.	PUNCT
ejpam-4830	362	1	for	for	ADP
ejpam-4830	362	2	any	any	DET
ejpam-4830	362	3	(	(	PUNCT
ejpam-4830	362	4	x	x	NOUN
ejpam-4830	362	5	,	,	PUNCT
ejpam-4830	362	6	j	j	NOUN
ejpam-4830	362	7	)	)	PUNCT
ejpam-4830	362	8	∈	∈	PROPN
ejpam-4830	362	9	(	(	PUNCT
ejpam-4830	362	10	0,∞)×m	0,∞)×m	NOUN
ejpam-4830	362	11	,	,	PUNCT
ejpam-4830	362	12	the	the	DET
ejpam-4830	362	13	mapping	mapping	NOUN
ejpam-4830	362	14	t	t	NOUN
ejpam-4830	362	15	7→	7→	NUM
ejpam-4830	362	16	f	f	PROPN
ejpam-4830	362	17	(	(	PUNCT
ejpam-4830	362	18	t	t	PROPN
ejpam-4830	362	19	,	,	PUNCT
ejpam-4830	362	20	x	x	PROPN
ejpam-4830	362	21	,	,	PUNCT
ejpam-4830	362	22	j	j	NOUN
ejpam-4830	362	23	)	)	PUNCT
ejpam-4830	362	24	=	=	SYM
ejpam-4830	362	25	v	v	X
ejpam-4830	362	26	(	(	PUNCT
ejpam-4830	362	27	t	t	PROPN
ejpam-4830	362	28	,	,	PUNCT
ejpam-4830	362	29	x	x	PROPN
ejpam-4830	362	30	,	,	PUNCT
ejpam-4830	362	31	j)−gµc(t	j)−gµc(t	PROPN
ejpam-4830	362	32	,	,	PUNCT
ejpam-4830	362	33	x	x	PROPN
ejpam-4830	362	34	,	,	PUNCT
ejpam-4830	362	35	j	j	PROPN
ejpam-4830	362	36	)	)	PUNCT
ejpam-4830	362	37	(	(	PUNCT
ejpam-4830	362	38	47	47	NUM
ejpam-4830	362	39	)	)	PUNCT
ejpam-4830	362	40	is	be	AUX
ejpam-4830	362	41	nonincreasing	nonincrease	VERB
ejpam-4830	362	42	in	in	ADP
ejpam-4830	362	43	t	t	PROPN
ejpam-4830	362	44	∈	∈	PROPN
ejpam-4830	363	1	[	[	X
ejpam-4830	363	2	0	0	NUM
ejpam-4830	363	3	,	,	PUNCT
ejpam-4830	363	4	t	t	X
ejpam-4830	363	5	]	]	PUNCT
ejpam-4830	363	6	.	.	PUNCT
ejpam-4830	364	1	proof	proof	NOUN
ejpam-4830	364	2	.	.	PUNCT
ejpam-4830	365	1	let	let	VERB
ejpam-4830	365	2	s1	s1	NOUN
ejpam-4830	365	3	,	,	PUNCT
ejpam-4830	365	4	s2	s2	NOUN
ejpam-4830	365	5	∈	∈	PROPN
ejpam-4830	366	1	[	[	X
ejpam-4830	366	2	0	0	NUM
ejpam-4830	366	3	,	,	PUNCT
ejpam-4830	366	4	t	t	PROPN
ejpam-4830	366	5	−	−	PROPN
ejpam-4830	366	6	t	t	PROPN
ejpam-4830	366	7	]	]	PUNCT
ejpam-4830	366	8	with	with	ADP
ejpam-4830	366	9	s1	s1	PROPN
ejpam-4830	366	10	<	<	X
ejpam-4830	366	11	s2	s2	NOUN
ejpam-4830	366	12	and	and	CCONJ
ejpam-4830	366	13	consider	consider	VERB
ejpam-4830	366	14	the	the	DET
ejpam-4830	366	15	stopping	stopping	NOUN
ejpam-4830	366	16	time	time	NOUN
ejpam-4830	366	17	τs2	τs2	NOUN
ejpam-4830	366	18	=	=	SYM
ejpam-4830	366	19	τd(s2	τd(s2	X
ejpam-4830	366	20	,	,	PUNCT
ejpam-4830	366	21	x	x	NOUN
ejpam-4830	366	22	,	,	PUNCT
ejpam-4830	366	23	j	j	NOUN
ejpam-4830	366	24	)	)	PUNCT
ejpam-4830	366	25	∈	∈	PROPN
ejpam-4830	367	1	[	[	X
ejpam-4830	367	2	0	0	NUM
ejpam-4830	367	3	,	,	PUNCT
ejpam-4830	367	4	t	t	NOUN
ejpam-4830	367	5	−	−	PROPN
ejpam-4830	367	6	s2	s2	PROPN
ejpam-4830	367	7	]	]	PUNCT
ejpam-4830	367	8	.	.	PUNCT
ejpam-4830	368	1	from	from	ADP
ejpam-4830	368	2	definition	definition	NOUN
ejpam-4830	368	3	of	of	ADP
ejpam-4830	368	4	the	the	DET
ejpam-4830	368	5	function	function	NOUN
ejpam-4830	368	6	f	f	PROPN
ejpam-4830	368	7	in	in	ADP
ejpam-4830	368	8	(	(	PUNCT
ejpam-4830	368	9	23	23	NUM
ejpam-4830	368	10	)	)	PUNCT
ejpam-4830	368	11	and	and	CCONJ
ejpam-4830	368	12	replacing	replace	VERB
ejpam-4830	368	13	τu	τu	ADP
ejpam-4830	368	14	with	with	ADP
ejpam-4830	368	15	τs2	τs2	NOUN
ejpam-4830	368	16	in	in	ADP
ejpam-4830	368	17	(	(	PUNCT
ejpam-4830	368	18	42	42	NUM
ejpam-4830	368	19	)	)	PUNCT
ejpam-4830	368	20	,	,	PUNCT
ejpam-4830	368	21	we	we	PRON
ejpam-4830	368	22	have	have	VERB
ejpam-4830	368	23	f	f	PROPN
ejpam-4830	368	24	(	(	PUNCT
ejpam-4830	368	25	s2	s2	PROPN
ejpam-4830	368	26	,	,	PUNCT
ejpam-4830	368	27	x	x	NOUN
ejpam-4830	368	28	,	,	PUNCT
ejpam-4830	368	29	j	j	NOUN
ejpam-4830	368	30	)	)	PUNCT
ejpam-4830	368	31	=	=	SYM
ejpam-4830	368	32	v	v	X
ejpam-4830	368	33	(	(	PUNCT
ejpam-4830	368	34	s2	s2	PROPN
ejpam-4830	368	35	,	,	PUNCT
ejpam-4830	368	36	x	x	X
ejpam-4830	368	37	,	,	PUNCT
ejpam-4830	368	38	j)−gµc(s2	j)−gµc(s2	PROPN
ejpam-4830	368	39	,	,	PUNCT
ejpam-4830	368	40	x	x	PROPN
ejpam-4830	368	41	,	,	PUNCT
ejpam-4830	368	42	j	j	NOUN
ejpam-4830	368	43	)	)	PUNCT
ejpam-4830	368	44	=	=	SYM
ejpam-4830	369	1	e	e	X
ejpam-4830	369	2	[	[	PUNCT
ejpam-4830	369	3	e−rτs2gµc(s2	e−rτs2gµc(s2	NOUN
ejpam-4830	369	4	+	+	X
ejpam-4830	369	5	τs2	τs2	NOUN
ejpam-4830	369	6	,	,	PUNCT
ejpam-4830	369	7	xs+τs2	xs+τs2	NOUN
ejpam-4830	369	8	,	,	PUNCT
ejpam-4830	369	9	αs+τs2	αs+τs2	NOUN
ejpam-4830	369	10	)	)	PUNCT
ejpam-4830	370	1	∣∣∣αs2	∣∣∣αs2	PROPN
ejpam-4830	370	2	=	=	SYM
ejpam-4830	370	3	j	j	PROPN
ejpam-4830	370	4	]	]	PUNCT
ejpam-4830	370	5	−gµc(s2	−gµc(s2	PROPN
ejpam-4830	370	6	,	,	PUNCT
ejpam-4830	370	7	x	x	X
ejpam-4830	370	8	,	,	PUNCT
ejpam-4830	370	9	j	j	NOUN
ejpam-4830	370	10	)	)	PUNCT
ejpam-4830	370	11	=	=	PUNCT
ejpam-4830	371	1	e	e	X
ejpam-4830	371	2	[	[	X
ejpam-4830	371	3	∫	∫	PROPN
ejpam-4830	371	4	s2+τs2	s2+τs2	PROPN
ejpam-4830	371	5	s2	s2	PROPN
ejpam-4830	371	6	e−rulgµc(u	e−rulgµc(u	PROPN
ejpam-4830	371	7	,	,	PUNCT
ejpam-4830	371	8	xu	xu	PROPN
ejpam-4830	371	9	,	,	PUNCT
ejpam-4830	371	10	αu)du	αu)du	PROPN
ejpam-4830	371	11	∣∣∣αs2	∣∣∣αs2	PROPN
ejpam-4830	371	12	=	=	SYM
ejpam-4830	371	13	j	j	PROPN
ejpam-4830	371	14	]	]	PUNCT
ejpam-4830	372	1	=	=	PUNCT
ejpam-4830	372	2	e	e	X
ejpam-4830	373	1	[	[	X
ejpam-4830	373	2	∫	∫	X
ejpam-4830	373	3	τs2	τs2	NOUN
ejpam-4830	373	4	0	0	PUNCT
ejpam-4830	373	5	e−rulgµc(s2	e−rulgµc(s2	PROPN
ejpam-4830	373	6	+	+	CCONJ
ejpam-4830	373	7	u	u	PROPN
ejpam-4830	373	8	,	,	PUNCT
ejpam-4830	373	9	xs2+u	xs2+u	PROPN
ejpam-4830	373	10	,	,	PUNCT
ejpam-4830	373	11	αs2+u)du	αs2+u)du	PROPN
ejpam-4830	373	12	∣∣∣α0	∣∣∣α0	PROPN
ejpam-4830	373	13	=	=	SYM
ejpam-4830	373	14	j	j	PROPN
ejpam-4830	373	15	]	]	PUNCT
ejpam-4830	373	16	.	.	PUNCT
ejpam-4830	374	1	(	(	PUNCT
ejpam-4830	374	2	48	48	NUM
ejpam-4830	374	3	)	)	PUNCT
ejpam-4830	374	4	combining	combine	VERB
ejpam-4830	374	5	(	(	PUNCT
ejpam-4830	374	6	48	48	NUM
ejpam-4830	374	7	)	)	PUNCT
ejpam-4830	374	8	with	with	ADP
ejpam-4830	374	9	(	(	PUNCT
ejpam-4830	374	10	49	49	NUM
ejpam-4830	374	11	)	)	PUNCT
ejpam-4830	374	12	below	below	ADP
ejpam-4830	374	13	f	f	PROPN
ejpam-4830	374	14	(	(	PUNCT
ejpam-4830	374	15	s1	s1	PROPN
ejpam-4830	374	16	,	,	PUNCT
ejpam-4830	374	17	x	x	NOUN
ejpam-4830	374	18	,	,	PUNCT
ejpam-4830	374	19	j	j	NOUN
ejpam-4830	374	20	)	)	PUNCT
ejpam-4830	374	21	=	=	SYM
ejpam-4830	374	22	v	v	X
ejpam-4830	374	23	(	(	PUNCT
ejpam-4830	374	24	s1	s1	NOUN
ejpam-4830	374	25	,	,	PUNCT
ejpam-4830	374	26	x	x	PROPN
ejpam-4830	374	27	,	,	PUNCT
ejpam-4830	374	28	j)−gµc(s1	j)−gµc(s1	PROPN
ejpam-4830	374	29	,	,	PUNCT
ejpam-4830	374	30	x	x	PROPN
ejpam-4830	374	31	,	,	PUNCT
ejpam-4830	374	32	j	j	PROPN
ejpam-4830	374	33	)	)	PUNCT
ejpam-4830	374	34	f.	f.	PROPN
ejpam-4830	374	35	sumalpong	sumalpong	PROPN
ejpam-4830	374	36	,	,	PUNCT
ejpam-4830	374	37	m.	m.	PROPN
ejpam-4830	374	38	frondoza	frondoza	PROPN
ejpam-4830	374	39	,	,	PUNCT
ejpam-4830	374	40	n.l	n.l	PROPN
ejpam-4830	374	41	.	.	PROPN
ejpam-4830	374	42	sayson	sayson	PROPN
ejpam-4830	374	43	/	/	SYM
ejpam-4830	374	44	eur	eur	PROPN
ejpam-4830	374	45	.	.	PUNCT
ejpam-4830	375	1	j.	j.	PROPN
ejpam-4830	375	2	pure	pure	PROPN
ejpam-4830	375	3	appl	appl	PROPN
ejpam-4830	375	4	.	.	PROPN
ejpam-4830	375	5	math	math	PROPN
ejpam-4830	375	6	,	,	PUNCT
ejpam-4830	375	7	16	16	NUM
ejpam-4830	375	8	(	(	PUNCT
ejpam-4830	375	9	3	3	NUM
ejpam-4830	375	10	)	)	PUNCT
ejpam-4830	375	11	(	(	PUNCT
ejpam-4830	375	12	2023	2023	NUM
ejpam-4830	375	13	)	)	PUNCT
ejpam-4830	375	14	,	,	PUNCT
ejpam-4830	375	15	1830	1830	NUM
ejpam-4830	375	16	-	-	SYM
ejpam-4830	375	17	1847	1847	NUM
ejpam-4830	375	18	1844	1844	NUM
ejpam-4830	375	19	≥	≥	NOUN
ejpam-4830	375	20	e	e	X
ejpam-4830	375	21	[	[	PUNCT
ejpam-4830	375	22	e−rτs2gµc(s1	e−rτs2gµc(s1	NOUN
ejpam-4830	375	23	+	+	CCONJ
ejpam-4830	375	24	τs2	τs2	NOUN
ejpam-4830	375	25	,	,	PUNCT
ejpam-4830	375	26	xs1+τs2	xs1+τs2	PROPN
ejpam-4830	375	27	,	,	PUNCT
ejpam-4830	375	28	αs1+τs2	αs1+τs2	NUM
ejpam-4830	375	29	)	)	PUNCT
ejpam-4830	376	1	∣∣∣αs1	∣∣∣αs1	PROPN
ejpam-4830	376	2	=	=	SYM
ejpam-4830	376	3	j	j	PROPN
ejpam-4830	376	4	]	]	PUNCT
ejpam-4830	376	5	−gµc(s1	−gµc(s1	NOUN
ejpam-4830	376	6	,	,	PUNCT
ejpam-4830	376	7	x	x	X
ejpam-4830	376	8	,	,	PUNCT
ejpam-4830	376	9	j	j	NOUN
ejpam-4830	376	10	)	)	PUNCT
ejpam-4830	376	11	=	=	PUNCT
ejpam-4830	377	1	e	e	X
ejpam-4830	377	2	[	[	X
ejpam-4830	377	3	∫	∫	X
ejpam-4830	377	4	s1+τs2	s1+τs2	PROPN
ejpam-4830	377	5	s1	s1	PROPN
ejpam-4830	377	6	e−rulgµc(u	e−rulgµc(u	PROPN
ejpam-4830	377	7	,	,	PUNCT
ejpam-4830	377	8	xu	xu	PROPN
ejpam-4830	377	9	,	,	PUNCT
ejpam-4830	377	10	αu)du	αu)du	X
ejpam-4830	377	11	∣∣∣αs1	∣∣∣αs1	NUM
ejpam-4830	377	12	=	=	SYM
ejpam-4830	377	13	j	j	PROPN
ejpam-4830	377	14	]	]	PUNCT
ejpam-4830	378	1	=	=	PUNCT
ejpam-4830	378	2	e	e	X
ejpam-4830	378	3	[	[	X
ejpam-4830	378	4	∫	∫	X
ejpam-4830	378	5	τs2	τs2	NOUN
ejpam-4830	378	6	0	0	PUNCT
ejpam-4830	378	7	e−rulgµc(s1	e−rulgµc(s1	PART
ejpam-4830	378	8	+	+	NUM
ejpam-4830	378	9	u	u	NOUN
ejpam-4830	378	10	,	,	PUNCT
ejpam-4830	378	11	xs1+u	xs1+u	PROPN
ejpam-4830	378	12	,	,	PUNCT
ejpam-4830	378	13	αs1+u)du	αs1+u)du	PROPN
ejpam-4830	378	14	∣∣∣α0	∣∣∣α0	PROPN
ejpam-4830	378	15	=	=	SYM
ejpam-4830	378	16	j	j	PROPN
ejpam-4830	378	17	]	]	PUNCT
ejpam-4830	378	18	,	,	PUNCT
ejpam-4830	378	19	(	(	PUNCT
ejpam-4830	378	20	49	49	NUM
ejpam-4830	378	21	)	)	PUNCT
ejpam-4830	378	22	we	we	PRON
ejpam-4830	378	23	have	have	VERB
ejpam-4830	378	24	f	f	PROPN
ejpam-4830	378	25	(	(	PUNCT
ejpam-4830	378	26	s2	s2	PROPN
ejpam-4830	378	27	,	,	PUNCT
ejpam-4830	378	28	x	x	X
ejpam-4830	378	29	,	,	PUNCT
ejpam-4830	378	30	j)−	j)−	PROPN
ejpam-4830	378	31	f	f	PROPN
ejpam-4830	378	32	(	(	PUNCT
ejpam-4830	378	33	s1	s1	PROPN
ejpam-4830	378	34	,	,	PUNCT
ejpam-4830	378	35	x	x	NOUN
ejpam-4830	378	36	,	,	PUNCT
ejpam-4830	378	37	j	j	NOUN
ejpam-4830	378	38	)	)	PUNCT
ejpam-4830	378	39	≤	≤	PUNCT
ejpam-4830	379	1	e	e	X
ejpam-4830	380	1	[	[	X
ejpam-4830	380	2	∫	∫	X
ejpam-4830	380	3	τs2	τs2	NOUN
ejpam-4830	380	4	0	0	PUNCT
ejpam-4830	380	5	e−rulgµc(s2	e−rulgµc(s2	PROPN
ejpam-4830	380	6	+	+	CCONJ
ejpam-4830	380	7	u	u	PROPN
ejpam-4830	380	8	,	,	PUNCT
ejpam-4830	380	9	xs2+u	xs2+u	PROPN
ejpam-4830	380	10	,	,	PUNCT
ejpam-4830	380	11	αs2+u)du	αs2+u)du	PROPN
ejpam-4830	380	12	∣∣∣α0	∣∣∣α0	PROPN
ejpam-4830	380	13	=	=	SYM
ejpam-4830	380	14	j	j	PROPN
ejpam-4830	380	15	]	]	PUNCT
ejpam-4830	380	16	−e	−e	PUNCT
ejpam-4830	381	1	[	[	X
ejpam-4830	381	2	∫	∫	X
ejpam-4830	381	3	τs2	τs2	NOUN
ejpam-4830	381	4	0	0	PUNCT
ejpam-4830	381	5	e−rulgµc(s1	e−rulgµc(s1	PART
ejpam-4830	381	6	+	+	NUM
ejpam-4830	381	7	u	u	NOUN
ejpam-4830	381	8	,	,	PUNCT
ejpam-4830	381	9	xs1+u	xs1+u	PROPN
ejpam-4830	381	10	,	,	PUNCT
ejpam-4830	381	11	αs1+u)du	αs1+u)du	PROPN
ejpam-4830	381	12	∣∣∣α0	∣∣∣α0	PROPN
ejpam-4830	381	13	=	=	SYM
ejpam-4830	381	14	j	j	PROPN
ejpam-4830	381	15	]	]	PUNCT
ejpam-4830	381	16	≤	≤	NUM
ejpam-4830	381	17	e	e	X
ejpam-4830	382	1	[	[	X
ejpam-4830	382	2	∫	∫	X
ejpam-4830	382	3	τs2	τs2	NOUN
ejpam-4830	382	4	0	0	NUM
ejpam-4830	382	5	{	{	PUNCT
ejpam-4830	382	6	lgµc(s2	lgµc(s2	NOUN
ejpam-4830	382	7	+	+	CCONJ
ejpam-4830	382	8	u	u	NOUN
ejpam-4830	382	9	,	,	PUNCT
ejpam-4830	382	10	xs2+u	xs2+u	PROPN
ejpam-4830	382	11	,	,	PUNCT
ejpam-4830	382	12	αs2+u)du−	αs2+u)du−	VERB
ejpam-4830	382	13	lgµc(s1	lgµc(s1	VERB
ejpam-4830	382	14	+	+	X
ejpam-4830	382	15	u	u	NOUN
ejpam-4830	382	16	,	,	PUNCT
ejpam-4830	382	17	xs1+u	xs1+u	X
ejpam-4830	382	18	,	,	PUNCT
ejpam-4830	382	19	αs1+u)du	αs1+u)du	NOUN
ejpam-4830	382	20	}	}	PUNCT
ejpam-4830	382	21	∣∣∣α0	∣∣∣α0	NOUN
ejpam-4830	382	22	=	=	SYM
ejpam-4830	382	23	j	j	PROPN
ejpam-4830	382	24	]	]	PUNCT
ejpam-4830	382	25	.	.	PUNCT
ejpam-4830	383	1	from	from	ADP
ejpam-4830	383	2	relation	relation	NOUN
ejpam-4830	383	3	(	(	PUNCT
ejpam-4830	383	4	37	37	NUM
ejpam-4830	383	5	)	)	PUNCT
ejpam-4830	383	6	with	with	ADP
ejpam-4830	383	7	r	r	NOUN
ejpam-4830	383	8	<	<	X
ejpam-4830	383	9	µc	µc	ADP
ejpam-4830	383	10	,	,	PUNCT
ejpam-4830	383	11	since	since	SCONJ
ejpam-4830	383	12	t	t	PROPN
ejpam-4830	383	13	7→	7→	PROPN
ejpam-4830	383	14	gµc(t	gµc(t	PROPN
ejpam-4830	383	15	,	,	PUNCT
ejpam-4830	383	16	x	x	NOUN
ejpam-4830	383	17	,	,	PUNCT
ejpam-4830	383	18	j	j	NOUN
ejpam-4830	383	19	)	)	PUNCT
ejpam-4830	383	20	is	be	AUX
ejpam-4830	383	21	nondecreasing	nondecrease	VERB
ejpam-4830	383	22	on	on	ADP
ejpam-4830	383	23	[	[	X
ejpam-4830	383	24	0	0	NUM
ejpam-4830	383	25	,	,	PUNCT
ejpam-4830	383	26	t	t	X
ejpam-4830	383	27	]	]	PUNCT
ejpam-4830	383	28	,	,	PUNCT
ejpam-4830	383	29	we	we	PRON
ejpam-4830	383	30	say	say	VERB
ejpam-4830	383	31	that	that	SCONJ
ejpam-4830	383	32	lgµc(t	lgµc(t	PROPN
ejpam-4830	383	33	,	,	PUNCT
ejpam-4830	383	34	x	x	PROPN
ejpam-4830	383	35	,	,	PUNCT
ejpam-4830	383	36	j	j	PROPN
ejpam-4830	383	37	)	)	PUNCT
ejpam-4830	383	38	is	be	AUX
ejpam-4830	383	39	nonincreasing	nonincrease	VERB
ejpam-4830	383	40	in	in	ADP
ejpam-4830	383	41	t	t	PROPN
ejpam-4830	383	42	,	,	PUNCT
ejpam-4830	383	43	we	we	PRON
ejpam-4830	383	44	find	find	VERB
ejpam-4830	383	45	that	that	SCONJ
ejpam-4830	383	46	the	the	DET
ejpam-4830	383	47	right	right	ADJ
ejpam-4830	383	48	hand	hand	NOUN
ejpam-4830	383	49	side	side	NOUN
ejpam-4830	383	50	is	be	AUX
ejpam-4830	383	51	nonpositive	nonpositive	ADJ
ejpam-4830	383	52	,	,	PUNCT
ejpam-4830	383	53	thereby	thereby	ADV
ejpam-4830	383	54	conclude	conclude	VERB
ejpam-4830	383	55	that	that	SCONJ
ejpam-4830	383	56	f	f	PROPN
ejpam-4830	383	57	(	(	PUNCT
ejpam-4830	383	58	t	t	PROPN
ejpam-4830	383	59	,	,	PUNCT
ejpam-4830	383	60	x	x	PROPN
ejpam-4830	383	61	,	,	PUNCT
ejpam-4830	383	62	j	j	PROPN
ejpam-4830	383	63	)	)	PUNCT
ejpam-4830	383	64	is	be	AUX
ejpam-4830	383	65	nonincreasing	nonincrease	VERB
ejpam-4830	383	66	in	in	ADP
ejpam-4830	383	67	t	t	PROPN
ejpam-4830	383	68	∈	∈	PROPN
ejpam-4830	384	1	[	[	X
ejpam-4830	384	2	0	0	NUM
ejpam-4830	384	3	,	,	PUNCT
ejpam-4830	384	4	t	t	X
ejpam-4830	384	5	]	]	PUNCT
ejpam-4830	384	6	.	.	PUNCT
ejpam-4830	385	1	proposition	proposition	NOUN
ejpam-4830	385	2	3	3	NUM
ejpam-4830	385	3	.	.	PUNCT
ejpam-4830	386	1	the	the	DET
ejpam-4830	386	2	boundary	boundary	ADJ
ejpam-4830	386	3	function	function	NOUN
ejpam-4830	386	4	bd(t	bd(t	PROPN
ejpam-4830	386	5	,	,	PUNCT
ejpam-4830	386	6	j	j	NOUN
ejpam-4830	386	7	)	)	PUNCT
ejpam-4830	386	8	is	be	AUX
ejpam-4830	386	9	continuous	continuous	ADJ
ejpam-4830	386	10	in	in	ADP
ejpam-4830	386	11	t	t	PROPN
ejpam-4830	386	12	∈	∈	PROPN
ejpam-4830	387	1	[	[	X
ejpam-4830	387	2	0	0	NUM
ejpam-4830	387	3	,	,	PUNCT
ejpam-4830	387	4	t	t	X
ejpam-4830	387	5	]	]	PUNCT
ejpam-4830	387	6	for	for	ADP
ejpam-4830	387	7	all	all	DET
ejpam-4830	387	8	j	j	PROPN
ejpam-4830	387	9	∈	∈	PROPN
ejpam-4830	387	10	m.	m.	NOUN
ejpam-4830	387	11	proof	proof	NOUN
ejpam-4830	387	12	.	.	PUNCT
ejpam-4830	388	1	let	let	VERB
ejpam-4830	388	2	αt	αt	NOUN
ejpam-4830	388	3	=	=	SYM
ejpam-4830	388	4	j	j	PROPN
ejpam-4830	388	5	∈	∈	PROPN
ejpam-4830	388	6	m	m	AUX
ejpam-4830	388	7	be	be	AUX
ejpam-4830	388	8	fixed	fix	VERB
ejpam-4830	388	9	.	.	PUNCT
ejpam-4830	389	1	we	we	PRON
ejpam-4830	389	2	first	first	ADV
ejpam-4830	389	3	show	show	VERB
ejpam-4830	389	4	that	that	SCONJ
ejpam-4830	389	5	the	the	DET
ejpam-4830	389	6	boundary	boundary	ADJ
ejpam-4830	389	7	function	function	NOUN
ejpam-4830	389	8	bd(t	bd(t	PROPN
ejpam-4830	389	9	,	,	PUNCT
ejpam-4830	389	10	j	j	NOUN
ejpam-4830	389	11	)	)	PUNCT
ejpam-4830	389	12	is	be	AUX
ejpam-4830	389	13	leftcontinuous	leftcontinuous	ADJ
ejpam-4830	389	14	.	.	PUNCT
ejpam-4830	390	1	suppose	suppose	VERB
ejpam-4830	390	2	to	to	ADP
ejpam-4830	390	3	the	the	DET
ejpam-4830	390	4	contrary	contrary	NOUN
ejpam-4830	390	5	that	that	SCONJ
ejpam-4830	390	6	it	it	PRON
ejpam-4830	390	7	is	be	AUX
ejpam-4830	390	8	not	not	PART
ejpam-4830	390	9	left	leave	VERB
ejpam-4830	390	10	-	-	PUNCT
ejpam-4830	390	11	continuous	continuous	ADJ
ejpam-4830	390	12	at	at	ADP
ejpam-4830	390	13	time	time	NOUN
ejpam-4830	390	14	t	t	PROPN
ejpam-4830	390	15	=	=	SYM
ejpam-4830	390	16	t0	t0	PROPN
ejpam-4830	390	17	.	.	PUNCT
ejpam-4830	391	1	consider	consider	VERB
ejpam-4830	391	2	the	the	DET
ejpam-4830	391	3	following	follow	VERB
ejpam-4830	391	4	cases	case	NOUN
ejpam-4830	391	5	:	:	PUNCT
ejpam-4830	391	6	case	case	NOUN
ejpam-4830	391	7	1	1	NUM
ejpam-4830	391	8	.	.	X
ejpam-4830	392	1	bd(t0−	bd(t0−	PROPN
ejpam-4830	392	2	,	,	PUNCT
ejpam-4830	392	3	j	j	PROPN
ejpam-4830	392	4	)	)	PUNCT
ejpam-4830	392	5	<	<	X
ejpam-4830	392	6	bd(t0	bd(t0	PROPN
ejpam-4830	392	7	,	,	PUNCT
ejpam-4830	392	8	j	j	NOUN
ejpam-4830	392	9	)	)	PUNCT
ejpam-4830	392	10	let	let	VERB
ejpam-4830	392	11	(	(	PUNCT
ejpam-4830	392	12	t′	t′	NUM
ejpam-4830	392	13	,	,	PUNCT
ejpam-4830	392	14	x′	x′	NUM
ejpam-4830	392	15	,	,	PUNCT
ejpam-4830	392	16	j	j	PROPN
ejpam-4830	392	17	)	)	PUNCT
ejpam-4830	392	18	∈	∈	PROPN
ejpam-4830	392	19	(	(	PUNCT
ejpam-4830	392	20	0	0	NUM
ejpam-4830	392	21	,	,	PUNCT
ejpam-4830	392	22	t0)×(bd(t0−	t0)×(bd(t0−	PROPN
ejpam-4830	392	23	,	,	PUNCT
ejpam-4830	392	24	j	j	PROPN
ejpam-4830	392	25	)	)	PUNCT
ejpam-4830	392	26	,	,	PUNCT
ejpam-4830	392	27	bd(t0	bd(t0	PROPN
ejpam-4830	392	28	,	,	PUNCT
ejpam-4830	392	29	j))×m	j))×m	ADJ
ejpam-4830	392	30	be	be	AUX
ejpam-4830	392	31	a	a	DET
ejpam-4830	392	32	point	point	NOUN
ejpam-4830	392	33	in	in	ADP
ejpam-4830	392	34	the	the	DET
ejpam-4830	392	35	continuation	continuation	NOUN
ejpam-4830	392	36	set	set	VERB
ejpam-4830	392	37	c	c	PROPN
ejpam-4830	392	38	with	with	ADP
ejpam-4830	392	39	t′	t′	NOUN
ejpam-4830	392	40	close	close	ADJ
ejpam-4830	392	41	to	to	ADP
ejpam-4830	392	42	t0	t0	PROPN
ejpam-4830	392	43	and	and	CCONJ
ejpam-4830	392	44	t′	t′	NUM
ejpam-4830	392	45	↑	↑	PROPN
ejpam-4830	392	46	t0	t0	PROPN
ejpam-4830	392	47	.	.	PUNCT
ejpam-4830	393	1	we	we	PRON
ejpam-4830	393	2	know	know	VERB
ejpam-4830	393	3	that	that	SCONJ
ejpam-4830	393	4	,	,	PUNCT
ejpam-4830	393	5	by	by	ADP
ejpam-4830	393	6	lemma	lemma	PROPN
ejpam-4830	393	7	4	4	NUM
ejpam-4830	393	8	,	,	PUNCT
ejpam-4830	393	9	x	x	PROPN
ejpam-4830	393	10	7→	7→	X
ejpam-4830	393	11	∂v	∂v	NOUN
ejpam-4830	393	12	∂x	∂x	PROPN
ejpam-4830	393	13	and	and	CCONJ
ejpam-4830	393	14	x	x	SYM
ejpam-4830	393	15	7→	7→	NUM
ejpam-4830	393	16	∂gµc	∂gµc	PRON
ejpam-4830	393	17	∂x	∂x	PROPN
ejpam-4830	393	18	are	be	AUX
ejpam-4830	393	19	both	both	ADV
ejpam-4830	393	20	continuous	continuous	ADJ
ejpam-4830	393	21	.	.	PUNCT
ejpam-4830	394	1	since	since	SCONJ
ejpam-4830	394	2	both	both	DET
ejpam-4830	394	3	∂v	∂v	PROPN
ejpam-4830	394	4	∂x	∂x	PROPN
ejpam-4830	394	5	and	and	CCONJ
ejpam-4830	394	6	∂gµc	∂gµc	NOUN
ejpam-4830	394	7	∂x	∂x	PROPN
ejpam-4830	394	8	are	be	AUX
ejpam-4830	394	9	bounded	bound	VERB
ejpam-4830	394	10	by	by	ADP
ejpam-4830	394	11	−p(y	−p(y	NOUN
ejpam-4830	394	12	≤	≤	X
ejpam-4830	394	13	k	k	X
ejpam-4830	394	14	)	)	PUNCT
ejpam-4830	394	15	for	for	ADP
ejpam-4830	394	16	(	(	PUNCT
ejpam-4830	394	17	t	t	PROPN
ejpam-4830	394	18	,	,	PUNCT
ejpam-4830	394	19	y	y	PROPN
ejpam-4830	394	20	,	,	PUNCT
ejpam-4830	394	21	j	j	PROPN
ejpam-4830	394	22	)	)	PUNCT
ejpam-4830	394	23	∈	∈	PROPN
ejpam-4830	395	1	d	d	NOUN
ejpam-4830	395	2	,	,	PUNCT
ejpam-4830	395	3	by	by	ADP
ejpam-4830	395	4	newton	newton	PROPN
ejpam-4830	395	5	-	-	PUNCT
ejpam-4830	395	6	leibniz	leibniz	PROPN
ejpam-4830	395	7	formula	formula	NOUN
ejpam-4830	395	8	and	and	CCONJ
ejpam-4830	395	9	lemma	lemma	PROPN
ejpam-4830	395	10	6	6	NUM
ejpam-4830	395	11	we	we	PRON
ejpam-4830	395	12	have	have	VERB
ejpam-4830	395	13	0	0	NUM
ejpam-4830	395	14	<	<	X
ejpam-4830	395	15	∫	∫	PROPN
ejpam-4830	395	16	bd(t0,j	bd(t0,j	PROPN
ejpam-4830	395	17	)	)	PUNCT
ejpam-4830	395	18	x′	x′	PROPN
ejpam-4830	396	1	[	[	PUNCT
ejpam-4830	396	2	vx(t	vx(t	PROPN
ejpam-4830	396	3	′	′	NUM
ejpam-4830	396	4	,	,	PUNCT
ejpam-4830	396	5	u	u	NOUN
ejpam-4830	396	6	,	,	PUNCT
ejpam-4830	396	7	j)−gµc	j)−gµc	X
ejpam-4830	396	8	x	x	SYM
ejpam-4830	396	9	(	(	PUNCT
ejpam-4830	396	10	t′	t′	NUM
ejpam-4830	396	11	,	,	PUNCT
ejpam-4830	396	12	u	u	NOUN
ejpam-4830	396	13	,	,	PUNCT
ejpam-4830	396	14	j	j	PROPN
ejpam-4830	396	15	)	)	PUNCT
ejpam-4830	396	16	]	]	PUNCT
ejpam-4830	397	1	du	du	PROPN
ejpam-4830	397	2	=	=	SYM
ejpam-4830	397	3	gµc(t′	gµc(t′	PROPN
ejpam-4830	397	4	,	,	PUNCT
ejpam-4830	397	5	x′	x′	NUM
ejpam-4830	397	6	,	,	PUNCT
ejpam-4830	397	7	j)−	j)−	PROPN
ejpam-4830	397	8	v	v	PROPN
ejpam-4830	397	9	(	(	PUNCT
ejpam-4830	397	10	t′	t′	NUM
ejpam-4830	397	11	,	,	PUNCT
ejpam-4830	397	12	x′	x′	NUM
ejpam-4830	397	13	,	,	PUNCT
ejpam-4830	397	14	j	j	PROPN
ejpam-4830	397	15	)	)	PUNCT
ejpam-4830	397	16	as	as	ADP
ejpam-4830	397	17	t′	t′	NUM
ejpam-4830	397	18	→	→	SYM
ejpam-4830	397	19	t0	t0	PROPN
ejpam-4830	397	20	.	.	PUNCT
ejpam-4830	398	1	this	this	PRON
ejpam-4830	398	2	implies	imply	VERB
ejpam-4830	398	3	that	that	SCONJ
ejpam-4830	398	4	v	v	X
ejpam-4830	398	5	(	(	PUNCT
ejpam-4830	398	6	t0	t0	PROPN
ejpam-4830	398	7	,	,	PUNCT
ejpam-4830	398	8	x	x	PROPN
ejpam-4830	398	9	′	′	NUM
ejpam-4830	398	10	,	,	PUNCT
ejpam-4830	398	11	j	j	PROPN
ejpam-4830	398	12	)	)	PUNCT
ejpam-4830	398	13	<	<	X
ejpam-4830	398	14	gµc(t0	gµc(t0	PROPN
ejpam-4830	398	15	,	,	PUNCT
ejpam-4830	398	16	x	x	PROPN
ejpam-4830	398	17	′	′	NUM
ejpam-4830	398	18	,	,	PUNCT
ejpam-4830	398	19	j	j	PROPN
ejpam-4830	398	20	)	)	PUNCT
ejpam-4830	398	21	which	which	PRON
ejpam-4830	398	22	contradicts	contradict	VERB
ejpam-4830	398	23	the	the	DET
ejpam-4830	398	24	fact	fact	NOUN
ejpam-4830	398	25	that	that	SCONJ
ejpam-4830	398	26	(	(	PUNCT
ejpam-4830	398	27	t0	t0	NOUN
ejpam-4830	398	28	,	,	PUNCT
ejpam-4830	398	29	x	x	PROPN
ejpam-4830	398	30	′	′	NUM
ejpam-4830	398	31	,	,	PUNCT
ejpam-4830	398	32	j	j	NOUN
ejpam-4830	398	33	)	)	PUNCT
ejpam-4830	398	34	∈	∈	PROPN
ejpam-4830	398	35	d	d	NOUN
ejpam-4830	398	36	since	since	SCONJ
ejpam-4830	398	37	x′	x′	PROPN
ejpam-4830	398	38	<	<	X
ejpam-4830	398	39	bd(t0	bd(t0	PROPN
ejpam-4830	398	40	,	,	PUNCT
ejpam-4830	398	41	j	j	PROPN
ejpam-4830	398	42	)	)	PUNCT
ejpam-4830	398	43	,	,	PUNCT
ejpam-4830	398	44	i.e.	i.e.	X
ejpam-4830	398	45	,	,	PUNCT
ejpam-4830	398	46	v	v	INTJ
ejpam-4830	398	47	(	(	PUNCT
ejpam-4830	398	48	t0	t0	PROPN
ejpam-4830	398	49	,	,	PUNCT
ejpam-4830	398	50	x	x	PROPN
ejpam-4830	398	51	′	′	NUM
ejpam-4830	398	52	,	,	PUNCT
ejpam-4830	398	53	j	j	NOUN
ejpam-4830	398	54	)	)	PUNCT
ejpam-4830	398	55	=	=	SYM
ejpam-4830	398	56	gµc(t0	gµc(t0	PROPN
ejpam-4830	398	57	,	,	PUNCT
ejpam-4830	398	58	x	x	PROPN
ejpam-4830	398	59	′	′	NUM
ejpam-4830	398	60	,	,	PUNCT
ejpam-4830	398	61	j	j	PROPN
ejpam-4830	398	62	)	)	PUNCT
ejpam-4830	398	63	.	.	PUNCT
ejpam-4830	399	1	case	case	NOUN
ejpam-4830	399	2	2	2	X
ejpam-4830	399	3	.	.	X
ejpam-4830	400	1	bd(t0−	bd(t0−	PROPN
ejpam-4830	400	2	,	,	PUNCT
ejpam-4830	400	3	j	j	PROPN
ejpam-4830	400	4	)	)	PUNCT
ejpam-4830	400	5	>	>	X
ejpam-4830	401	1	bd(t0	bd(t0	PROPN
ejpam-4830	401	2	,	,	PUNCT
ejpam-4830	401	3	j	j	PROPN
ejpam-4830	401	4	)	)	PUNCT
ejpam-4830	401	5	f.	f.	PROPN
ejpam-4830	401	6	sumalpong	sumalpong	PROPN
ejpam-4830	401	7	,	,	PUNCT
ejpam-4830	401	8	m.	m.	PROPN
ejpam-4830	401	9	frondoza	frondoza	PROPN
ejpam-4830	401	10	,	,	PUNCT
ejpam-4830	401	11	n.l	n.l	PROPN
ejpam-4830	401	12	.	.	PROPN
ejpam-4830	401	13	sayson	sayson	PROPN
ejpam-4830	401	14	/	/	SYM
ejpam-4830	401	15	eur	eur	PROPN
ejpam-4830	401	16	.	.	PUNCT
ejpam-4830	402	1	j.	j.	PROPN
ejpam-4830	402	2	pure	pure	PROPN
ejpam-4830	402	3	appl	appl	PROPN
ejpam-4830	402	4	.	.	PROPN
ejpam-4830	402	5	math	math	PROPN
ejpam-4830	402	6	,	,	PUNCT
ejpam-4830	402	7	16	16	NUM
ejpam-4830	402	8	(	(	PUNCT
ejpam-4830	402	9	3	3	NUM
ejpam-4830	402	10	)	)	PUNCT
ejpam-4830	402	11	(	(	PUNCT
ejpam-4830	402	12	2023	2023	NUM
ejpam-4830	402	13	)	)	PUNCT
ejpam-4830	402	14	,	,	PUNCT
ejpam-4830	402	15	1830	1830	NUM
ejpam-4830	402	16	-	-	SYM
ejpam-4830	402	17	1847	1847	NUM
ejpam-4830	402	18	1845	1845	NUM
ejpam-4830	402	19	let	let	VERB
ejpam-4830	402	20	(	(	PUNCT
ejpam-4830	402	21	t∗	t∗	NOUN
ejpam-4830	402	22	,	,	PUNCT
ejpam-4830	402	23	x∗	x∗	PROPN
ejpam-4830	402	24	,	,	PUNCT
ejpam-4830	402	25	j	j	NOUN
ejpam-4830	402	26	)	)	PUNCT
ejpam-4830	402	27	∈	∈	PROPN
ejpam-4830	402	28	(	(	PUNCT
ejpam-4830	402	29	0	0	NUM
ejpam-4830	402	30	,	,	PUNCT
ejpam-4830	402	31	t0	t0	PROPN
ejpam-4830	402	32	)	)	PUNCT
ejpam-4830	402	33	×	×	NOUN
ejpam-4830	402	34	(	(	PUNCT
ejpam-4830	402	35	bd(t0	bd(t0	PROPN
ejpam-4830	402	36	,	,	PUNCT
ejpam-4830	402	37	j	j	PROPN
ejpam-4830	402	38	)	)	PUNCT
ejpam-4830	402	39	,	,	PUNCT
ejpam-4830	402	40	bd(t0−	bd(t0−	PROPN
ejpam-4830	402	41	,	,	PUNCT
ejpam-4830	402	42	j	j	NOUN
ejpam-4830	402	43	)	)	PUNCT
ejpam-4830	402	44	×m	×m	NOUN
ejpam-4830	402	45	)	)	PUNCT
ejpam-4830	402	46	be	be	AUX
ejpam-4830	402	47	a	a	DET
ejpam-4830	402	48	point	point	NOUN
ejpam-4830	402	49	on	on	ADP
ejpam-4830	402	50	the	the	DET
ejpam-4830	402	51	stopping	stopping	NOUN
ejpam-4830	402	52	set	set	VERB
ejpam-4830	402	53	d	d	NOUN
ejpam-4830	402	54	with	with	ADP
ejpam-4830	402	55	t∗	t∗	NOUN
ejpam-4830	402	56	close	close	ADJ
ejpam-4830	402	57	to	to	ADP
ejpam-4830	402	58	t0	t0	PROPN
ejpam-4830	402	59	and	and	CCONJ
ejpam-4830	402	60	t∗	t∗	PROPN
ejpam-4830	402	61	↑	↑	PROPN
ejpam-4830	402	62	t0	t0	PROPN
ejpam-4830	402	63	.	.	PUNCT
ejpam-4830	403	1	by	by	ADP
ejpam-4830	403	2	(	(	PUNCT
ejpam-4830	403	3	40	40	NUM
ejpam-4830	403	4	)	)	PUNCT
ejpam-4830	403	5	,	,	PUNCT
ejpam-4830	403	6	we	we	PRON
ejpam-4830	403	7	have	have	VERB
ejpam-4830	403	8	vx(t	vx(t	ADP
ejpam-4830	403	9	∗	∗	NOUN
ejpam-4830	403	10	,	,	PUNCT
ejpam-4830	403	11	x∗	x∗	PROPN
ejpam-4830	403	12	,	,	PUNCT
ejpam-4830	403	13	j	j	NOUN
ejpam-4830	403	14	)	)	PUNCT
ejpam-4830	403	15	=	=	SYM
ejpam-4830	403	16	gµc(t∗	gµc(t∗	NOUN
ejpam-4830	403	17	,	,	PUNCT
ejpam-4830	403	18	x∗	x∗	PROPN
ejpam-4830	403	19	,	,	PUNCT
ejpam-4830	403	20	j	j	NOUN
ejpam-4830	403	21	)	)	PUNCT
ejpam-4830	403	22	on	on	ADP
ejpam-4830	403	23	d.	d.	PROPN
ejpam-4830	403	24	similarly	similarly	ADV
ejpam-4830	403	25	,	,	PUNCT
ejpam-4830	403	26	by	by	ADP
ejpam-4830	403	27	newton	newton	PROPN
ejpam-4830	403	28	-	-	PUNCT
ejpam-4830	403	29	leibniz	leibniz	PROPN
ejpam-4830	403	30	formula	formula	NOUN
ejpam-4830	403	31	,	,	PUNCT
ejpam-4830	403	32	we	we	PRON
ejpam-4830	403	33	have	have	VERB
ejpam-4830	403	34	0	0	NUM
ejpam-4830	404	1	=	=	SYM
ejpam-4830	404	2	∫	∫	PROPN
ejpam-4830	404	3	x	x	PROPN
ejpam-4830	404	4	bd(t0,j	bd(t0,j	PROPN
ejpam-4830	404	5	)	)	PUNCT
ejpam-4830	405	1	[	[	X
ejpam-4830	405	2	vx(t	vx(t	ADP
ejpam-4830	405	3	∗	∗	NOUN
ejpam-4830	405	4	,	,	PUNCT
ejpam-4830	405	5	v	v	NOUN
ejpam-4830	405	6	,	,	PUNCT
ejpam-4830	405	7	j)−gµc	j)−gµc	X
ejpam-4830	405	8	x	x	X
ejpam-4830	405	9	(	(	PUNCT
ejpam-4830	405	10	t∗	t∗	PROPN
ejpam-4830	405	11	,	,	PUNCT
ejpam-4830	405	12	v	v	NOUN
ejpam-4830	405	13	,	,	PUNCT
ejpam-4830	405	14	j	j	PROPN
ejpam-4830	405	15	)	)	PUNCT
ejpam-4830	405	16	]	]	PUNCT
ejpam-4830	406	1	dv	dv	PROPN
ejpam-4830	406	2	=	=	PROPN
ejpam-4830	406	3	v	v	PROPN
ejpam-4830	406	4	(	(	PUNCT
ejpam-4830	406	5	t∗	t∗	PROPN
ejpam-4830	406	6	,	,	PUNCT
ejpam-4830	406	7	x∗	x∗	PROPN
ejpam-4830	406	8	,	,	PUNCT
ejpam-4830	406	9	j)−gµc(t∗	j)−gµc(t∗	PROPN
ejpam-4830	406	10	,	,	PUNCT
ejpam-4830	406	11	x∗	x∗	PROPN
ejpam-4830	406	12	,	,	PUNCT
ejpam-4830	406	13	j	j	NOUN
ejpam-4830	406	14	)	)	PUNCT
ejpam-4830	406	15	as	as	ADP
ejpam-4830	406	16	t∗	t∗	NOUN
ejpam-4830	406	17	→	→	SYM
ejpam-4830	406	18	t0	t0	PROPN
ejpam-4830	406	19	.	.	PUNCT
ejpam-4830	407	1	this	this	PRON
ejpam-4830	407	2	shows	show	VERB
ejpam-4830	407	3	that	that	SCONJ
ejpam-4830	407	4	v	v	X
ejpam-4830	407	5	(	(	PUNCT
ejpam-4830	407	6	t0	t0	PROPN
ejpam-4830	407	7	,	,	PUNCT
ejpam-4830	407	8	x	x	SYM
ejpam-4830	407	9	∗	∗	NOUN
ejpam-4830	407	10	,	,	PUNCT
ejpam-4830	407	11	j	j	NOUN
ejpam-4830	407	12	)	)	PUNCT
ejpam-4830	407	13	=	=	SYM
ejpam-4830	407	14	gµc(t0	gµc(t0	PROPN
ejpam-4830	407	15	,	,	PUNCT
ejpam-4830	407	16	x	x	SYM
ejpam-4830	407	17	∗	∗	NOUN
ejpam-4830	407	18	,	,	PUNCT
ejpam-4830	407	19	j	j	NOUN
ejpam-4830	407	20	)	)	PUNCT
ejpam-4830	407	21	which	which	PRON
ejpam-4830	407	22	contradicts	contradict	VERB
ejpam-4830	407	23	the	the	DET
ejpam-4830	407	24	fact	fact	NOUN
ejpam-4830	408	1	that	that	SCONJ
ejpam-4830	408	2	(	(	PUNCT
ejpam-4830	408	3	t0	t0	NOUN
ejpam-4830	408	4	,	,	PUNCT
ejpam-4830	408	5	x	x	SYM
ejpam-4830	408	6	∗	∗	NOUN
ejpam-4830	408	7	,	,	PUNCT
ejpam-4830	408	8	j	j	NOUN
ejpam-4830	408	9	)	)	PUNCT
ejpam-4830	408	10	∈	∈	PROPN
ejpam-4830	408	11	c	c	PROPN
ejpam-4830	408	12	since	since	SCONJ
ejpam-4830	408	13	x∗	x∗	PROPN
ejpam-4830	408	14	>	>	X
ejpam-4830	408	15	bd(t0	bd(t0	PROPN
ejpam-4830	408	16	,	,	PUNCT
ejpam-4830	408	17	j	j	PROPN
ejpam-4830	408	18	)	)	PUNCT
ejpam-4830	408	19	,	,	PUNCT
ejpam-4830	408	20	i.e.	i.e.	X
ejpam-4830	408	21	,	,	PUNCT
ejpam-4830	408	22	v	v	INTJ
ejpam-4830	408	23	(	(	PUNCT
ejpam-4830	408	24	t∗	t∗	NOUN
ejpam-4830	408	25	,	,	PUNCT
ejpam-4830	408	26	x∗	x∗	PROPN
ejpam-4830	408	27	,	,	PUNCT
ejpam-4830	408	28	j	j	NOUN
ejpam-4830	408	29	)	)	PUNCT
ejpam-4830	408	30	>	>	X
ejpam-4830	409	1	gµc(t∗	gµc(t∗	PROPN
ejpam-4830	409	2	,	,	PUNCT
ejpam-4830	409	3	x∗	x∗	PROPN
ejpam-4830	409	4	,	,	PUNCT
ejpam-4830	409	5	j	j	NOUN
ejpam-4830	409	6	)	)	PUNCT
ejpam-4830	409	7	.	.	PUNCT
ejpam-4830	410	1	therefore	therefore	ADV
ejpam-4830	410	2	,	,	PUNCT
ejpam-4830	410	3	in	in	ADP
ejpam-4830	410	4	either	either	DET
ejpam-4830	410	5	case	case	NOUN
ejpam-4830	410	6	,	,	PUNCT
ejpam-4830	410	7	bd	bd	PROPN
ejpam-4830	410	8	is	be	AUX
ejpam-4830	410	9	left	leave	VERB
ejpam-4830	410	10	-	-	PUNCT
ejpam-4830	410	11	continuous	continuous	ADJ
ejpam-4830	410	12	.	.	PUNCT
ejpam-4830	411	1	to	to	PART
ejpam-4830	411	2	prove	prove	VERB
ejpam-4830	411	3	the	the	DET
ejpam-4830	411	4	right	right	NOUN
ejpam-4830	411	5	-	-	PUNCT
ejpam-4830	411	6	continuity	continuity	NOUN
ejpam-4830	411	7	can	can	AUX
ejpam-4830	411	8	be	be	AUX
ejpam-4830	411	9	done	do	VERB
ejpam-4830	411	10	similarly	similarly	ADV
ejpam-4830	411	11	.	.	PUNCT
ejpam-4830	412	1	proposition	proposition	NOUN
ejpam-4830	412	2	4	4	NUM
ejpam-4830	412	3	.	.	PUNCT
ejpam-4830	413	1	the	the	DET
ejpam-4830	413	2	boundary	boundary	ADJ
ejpam-4830	413	3	function	function	NOUN
ejpam-4830	413	4	bd(t	bd(t	PROPN
ejpam-4830	413	5	,	,	PUNCT
ejpam-4830	413	6	j	j	NOUN
ejpam-4830	413	7	)	)	PUNCT
ejpam-4830	413	8	satisfies	satisfy	VERB
ejpam-4830	413	9	the	the	DET
ejpam-4830	413	10	volterra	volterra	NOUN
ejpam-4830	413	11	type	type	NOUN
ejpam-4830	413	12	equation	equation	NOUN
ejpam-4830	413	13	gµc(t	gµc(t	NOUN
ejpam-4830	413	14	,	,	PUNCT
ejpam-4830	413	15	bd(t	bd(t	NOUN
ejpam-4830	413	16	,	,	PUNCT
ejpam-4830	413	17	j	j	PROPN
ejpam-4830	413	18	)	)	PUNCT
ejpam-4830	413	19	,	,	PUNCT
ejpam-4830	413	20	j	j	NOUN
ejpam-4830	413	21	)	)	PUNCT
ejpam-4830	414	1	=	=	SYM
ejpam-4830	414	2	f	f	PROPN
ejpam-4830	414	3	(	(	PUNCT
ejpam-4830	414	4	t	t	PROPN
ejpam-4830	414	5	,	,	PUNCT
ejpam-4830	414	6	bd(t	bd(t	PROPN
ejpam-4830	414	7	,	,	PUNCT
ejpam-4830	414	8	j	j	NOUN
ejpam-4830	414	9	)	)	PUNCT
ejpam-4830	414	10	,	,	PUNCT
ejpam-4830	414	11	j)−	j)−	PROPN
ejpam-4830	414	12	∫	∫	PROPN
ejpam-4830	414	13	t	t	PROPN
ejpam-4830	414	14	t	t	PROPN
ejpam-4830	414	15	j(t	j(t	PROPN
ejpam-4830	414	16	,	,	PUNCT
ejpam-4830	414	17	bd(t	bd(t	PROPN
ejpam-4830	414	18	,	,	PUNCT
ejpam-4830	414	19	j	j	PROPN
ejpam-4830	414	20	)	)	PUNCT
ejpam-4830	414	21	,	,	PUNCT
ejpam-4830	414	22	u	u	NOUN
ejpam-4830	414	23	,	,	PUNCT
ejpam-4830	414	24	bd(u	bd(u	X
ejpam-4830	414	25	,	,	PUNCT
ejpam-4830	414	26	αu	αu	NOUN
ejpam-4830	414	27	)	)	PUNCT
ejpam-4830	414	28	,	,	PUNCT
ejpam-4830	414	29	αu)du	αu)du	PROPN
ejpam-4830	414	30	,	,	PUNCT
ejpam-4830	414	31	(	(	PUNCT
ejpam-4830	414	32	50	50	NUM
ejpam-4830	414	33	)	)	PUNCT
ejpam-4830	414	34	for	for	ADP
ejpam-4830	414	35	0	0	NUM
ejpam-4830	414	36	≤	≤	NUM
ejpam-4830	414	37	t	t	PROPN
ejpam-4830	414	38	≤	≤	PROPN
ejpam-4830	414	39	t	t	NOUN
ejpam-4830	414	40	,	,	PUNCT
ejpam-4830	414	41	where	where	SCONJ
ejpam-4830	414	42	f	f	PROPN
ejpam-4830	414	43	(	(	PUNCT
ejpam-4830	414	44	t	t	PROPN
ejpam-4830	414	45	,	,	PUNCT
ejpam-4830	414	46	x	x	PROPN
ejpam-4830	414	47	,	,	PUNCT
ejpam-4830	414	48	j	j	NOUN
ejpam-4830	414	49	)	)	PUNCT
ejpam-4830	414	50	=	=	SYM
ejpam-4830	414	51	e	e	X
ejpam-4830	414	52	[	[	PUNCT
ejpam-4830	414	53	(	(	PUNCT
ejpam-4830	414	54	k	k	NOUN
ejpam-4830	414	55	−xt	−xt	PROPN
ejpam-4830	414	56	)	)	PUNCT
ejpam-4830	415	1	+	+	CCONJ
ejpam-4830	415	2	∣∣∣αt	∣∣∣αt	X
ejpam-4830	415	3	=	=	SYM
ejpam-4830	415	4	j	j	PROPN
ejpam-4830	415	5	,	,	PUNCT
ejpam-4830	415	6	xt	xt	X
ejpam-4830	416	1	=	=	SYM
ejpam-4830	416	2	x	x	SYM
ejpam-4830	416	3	]	]	X
ejpam-4830	416	4	(	(	PUNCT
ejpam-4830	416	5	51	51	NUM
ejpam-4830	416	6	)	)	PUNCT
ejpam-4830	416	7	and	and	CCONJ
ejpam-4830	416	8	j(t	j(t	PROPN
ejpam-4830	416	9	,	,	PUNCT
ejpam-4830	416	10	x	x	X
ejpam-4830	416	11	,	,	PUNCT
ejpam-4830	416	12	u	u	NOUN
ejpam-4830	416	13	,	,	PUNCT
ejpam-4830	416	14	bd(u	bd(u	X
ejpam-4830	416	15	,	,	PUNCT
ejpam-4830	416	16	αu	αu	NOUN
ejpam-4830	416	17	)	)	PUNCT
ejpam-4830	416	18	,	,	PUNCT
ejpam-4830	416	19	αu	αu	NOUN
ejpam-4830	416	20	)	)	PUNCT
ejpam-4830	416	21	=	=	SYM
ejpam-4830	416	22	e	e	X
ejpam-4830	416	23	[	[	PUNCT
ejpam-4830	416	24	lxv	lxv	NOUN
ejpam-4830	416	25	(	(	PUNCT
ejpam-4830	416	26	u	u	NOUN
ejpam-4830	416	27	,	,	PUNCT
ejpam-4830	416	28	xu	xu	PROPN
ejpam-4830	416	29	,	,	PUNCT
ejpam-4830	416	30	j)i(xu	j)i(xu	X
ejpam-4830	416	31	<	<	X
ejpam-4830	416	32	bd(u	bd(u	PROPN
ejpam-4830	416	33	,	,	PUNCT
ejpam-4830	416	34	j	j	NOUN
ejpam-4830	416	35	)	)	PUNCT
ejpam-4830	416	36	)	)	PUNCT
ejpam-4830	416	37	∣∣∣αt	∣∣∣αt	X
ejpam-4830	417	1	=	=	SYM
ejpam-4830	417	2	j	j	PROPN
ejpam-4830	417	3	,	,	PUNCT
ejpam-4830	417	4	xt	xt	X
ejpam-4830	418	1	=	=	SYM
ejpam-4830	418	2	x	x	X
ejpam-4830	418	3	]	]	X
ejpam-4830	418	4	,	,	PUNCT
ejpam-4830	418	5	(	(	PUNCT
ejpam-4830	418	6	52	52	NUM
ejpam-4830	418	7	)	)	PUNCT
ejpam-4830	418	8	for	for	ADP
ejpam-4830	418	9	0	0	NUM
ejpam-4830	418	10	≤	≤	NUM
ejpam-4830	418	11	t	t	NOUN
ejpam-4830	418	12	≤	≤	NOUN
ejpam-4830	418	13	t	t	PROPN
ejpam-4830	418	14	and	and	CCONJ
ejpam-4830	418	15	x	x	PROPN
ejpam-4830	418	16	∈	∈	PROPN
ejpam-4830	418	17	(	(	PUNCT
ejpam-4830	418	18	0,∞	0,∞	NOUN
ejpam-4830	418	19	)	)	PUNCT
ejpam-4830	418	20	.	.	PUNCT
ejpam-4830	419	1	proof	proof	NOUN
ejpam-4830	419	2	.	.	PUNCT
ejpam-4830	420	1	from	from	ADP
ejpam-4830	420	2	relation	relation	NOUN
ejpam-4830	420	3	(	(	PUNCT
ejpam-4830	420	4	16	16	NUM
ejpam-4830	420	5	)	)	PUNCT
ejpam-4830	420	6	,	,	PUNCT
ejpam-4830	420	7	we	we	PRON
ejpam-4830	420	8	see	see	VERB
ejpam-4830	420	9	that	that	PRON
ejpam-4830	420	10	v	v	NOUN
ejpam-4830	420	11	(	(	PUNCT
ejpam-4830	420	12	t	t	PROPN
ejpam-4830	420	13	,	,	PUNCT
ejpam-4830	420	14	x	x	PROPN
ejpam-4830	420	15	,	,	PUNCT
ejpam-4830	420	16	j	j	PROPN
ejpam-4830	420	17	)	)	PUNCT
ejpam-4830	420	18	≥	≥	PROPN
ejpam-4830	421	1	gµc(t	gµc(t	NOUN
ejpam-4830	421	2	,	,	PUNCT
ejpam-4830	421	3	x	x	NOUN
ejpam-4830	421	4	,	,	PUNCT
ejpam-4830	421	5	j	j	PROPN
ejpam-4830	421	6	)	)	PUNCT
ejpam-4830	421	7	for	for	ADP
ejpam-4830	421	8	all	all	DET
ejpam-4830	421	9	(	(	PUNCT
ejpam-4830	421	10	t	t	PROPN
ejpam-4830	421	11	,	,	PUNCT
ejpam-4830	421	12	x	x	PROPN
ejpam-4830	421	13	,	,	PUNCT
ejpam-4830	421	14	j	j	NOUN
ejpam-4830	421	15	)	)	PUNCT
ejpam-4830	421	16	∈	∈	PROPN
ejpam-4830	422	1	[	[	X
ejpam-4830	422	2	0	0	NUM
ejpam-4830	422	3	,	,	PUNCT
ejpam-4830	422	4	t	t	X
ejpam-4830	422	5	]	]	X
ejpam-4830	422	6	×	×	NOUN
ejpam-4830	422	7	(	(	PUNCT
ejpam-4830	422	8	0,∞)×m	0,∞)×m	NUM
ejpam-4830	422	9	and	and	CCONJ
ejpam-4830	422	10	recall	recall	VERB
ejpam-4830	422	11	the	the	DET
ejpam-4830	422	12	continuation	continuation	NOUN
ejpam-4830	422	13	set	set	VERB
ejpam-4830	422	14	c	c	NOUN
ejpam-4830	422	15	=	=	SYM
ejpam-4830	422	16	dc	dc	PROPN
ejpam-4830	422	17	=	=	SYM
ejpam-4830	422	18	{	{	PUNCT
ejpam-4830	422	19	(	(	PUNCT
ejpam-4830	422	20	t	t	PROPN
ejpam-4830	422	21	,	,	PUNCT
ejpam-4830	422	22	x	x	PROPN
ejpam-4830	422	23	,	,	PUNCT
ejpam-4830	422	24	j	j	NOUN
ejpam-4830	422	25	)	)	PUNCT
ejpam-4830	422	26	∈	∈	PROPN
ejpam-4830	423	1	[	[	X
ejpam-4830	423	2	0	0	NUM
ejpam-4830	423	3	,	,	PUNCT
ejpam-4830	423	4	t	t	X
ejpam-4830	423	5	]	]	X
ejpam-4830	423	6	×	×	NOUN
ejpam-4830	423	7	(	(	PUNCT
ejpam-4830	423	8	0,∞)×m	0,∞)×m	ADJ
ejpam-4830	423	9	∣∣∣	∣∣∣	ADJ
ejpam-4830	423	10	v	v	NOUN
ejpam-4830	423	11	(	(	PUNCT
ejpam-4830	423	12	t	t	PROPN
ejpam-4830	423	13	,	,	PUNCT
ejpam-4830	423	14	x	x	NOUN
ejpam-4830	423	15	,	,	PUNCT
ejpam-4830	423	16	j	j	PROPN
ejpam-4830	423	17	)	)	PUNCT
ejpam-4830	423	18	>	>	X
ejpam-4830	424	1	gµc(t	gµc(t	PROPN
ejpam-4830	424	2	,	,	PUNCT
ejpam-4830	424	3	x	x	NOUN
ejpam-4830	424	4	,	,	PUNCT
ejpam-4830	424	5	j	j	NOUN
ejpam-4830	424	6	)	)	PUNCT
ejpam-4830	424	7	}	}	PUNCT
ejpam-4830	424	8	.	.	PUNCT
ejpam-4830	425	1	noting	note	VERB
ejpam-4830	425	2	that	that	SCONJ
ejpam-4830	425	3	the	the	DET
ejpam-4830	425	4	stopping	stopping	NOUN
ejpam-4830	425	5	time	time	NOUN
ejpam-4830	425	6	τd	τd	ADP
ejpam-4830	425	7	=	=	PUNCT
ejpam-4830	425	8	τd(t	τd(t	X
ejpam-4830	425	9	,	,	PUNCT
ejpam-4830	425	10	x	x	PROPN
ejpam-4830	425	11	,	,	PUNCT
ejpam-4830	425	12	j	j	NOUN
ejpam-4830	425	13	)	)	PUNCT
ejpam-4830	425	14	defined	define	VERB
ejpam-4830	425	15	in	in	ADP
ejpam-4830	425	16	(	(	PUNCT
ejpam-4830	425	17	21	21	NUM
ejpam-4830	425	18	)	)	PUNCT
ejpam-4830	425	19	is	be	AUX
ejpam-4830	425	20	optimal	optimal	ADJ
ejpam-4830	425	21	for	for	ADP
ejpam-4830	425	22	(	(	PUNCT
ejpam-4830	425	23	16	16	NUM
ejpam-4830	425	24	)	)	PUNCT
ejpam-4830	425	25	,	,	PUNCT
ejpam-4830	425	26	we	we	PRON
ejpam-4830	425	27	have	have	VERB
ejpam-4830	425	28	v	v	NUM
ejpam-4830	425	29	(	(	PUNCT
ejpam-4830	425	30	t	t	PROPN
ejpam-4830	425	31	,	,	PUNCT
ejpam-4830	425	32	x	x	X
ejpam-4830	425	33	,	,	PUNCT
ejpam-4830	425	34	i	i	NOUN
ejpam-4830	425	35	)	)	PUNCT
ejpam-4830	426	1	=	=	PUNCT
ejpam-4830	426	2	e	e	X
ejpam-4830	426	3	[	[	PUNCT
ejpam-4830	426	4	e−rτgµc(t+	e−rτgµc(t+	NOUN
ejpam-4830	426	5	τd	τd	NOUN
ejpam-4830	426	6	,	,	PUNCT
ejpam-4830	426	7	xt+τd	xt+τd	PROPN
ejpam-4830	426	8	,	,	PUNCT
ejpam-4830	426	9	j	j	NOUN
ejpam-4830	426	10	)	)	PUNCT
ejpam-4830	426	11	∣∣∣	∣∣∣	NOUN
ejpam-4830	426	12	αt	αt	PROPN
ejpam-4830	426	13	=	=	SYM
ejpam-4830	426	14	i	i	PROPN
ejpam-4830	426	15	,	,	PUNCT
ejpam-4830	426	16	xt	xt	X
ejpam-4830	427	1	=	=	SYM
ejpam-4830	427	2	x	x	X
ejpam-4830	427	3	]	]	PUNCT
ejpam-4830	427	4	.	.	PUNCT
ejpam-4830	428	1	it	it	PRON
ejpam-4830	428	2	is	be	AUX
ejpam-4830	428	3	well	well	ADV
ejpam-4830	428	4	known	know	VERB
ejpam-4830	428	5	from	from	ADP
ejpam-4830	428	6	the	the	DET
ejpam-4830	428	7	theory	theory	NOUN
ejpam-4830	428	8	of	of	ADP
ejpam-4830	428	9	markov	markov	NOUN
ejpam-4830	428	10	processes	process	VERB
ejpam-4830	428	11	that	that	PRON
ejpam-4830	428	12	v	v	NOUN
ejpam-4830	428	13	(	(	PUNCT
ejpam-4830	428	14	t	t	PROPN
ejpam-4830	428	15	,	,	PUNCT
ejpam-4830	428	16	x	x	X
ejpam-4830	428	17	,	,	PUNCT
ejpam-4830	428	18	i	i	PRON
ejpam-4830	428	19	)	)	PUNCT
ejpam-4830	428	20	is	be	AUX
ejpam-4830	428	21	c1,2	c1,2	ADJ
ejpam-4830	428	22	in	in	ADP
ejpam-4830	428	23	the	the	DET
ejpam-4830	428	24	continuation	continuation	NOUN
ejpam-4830	428	25	set	set	NOUN
ejpam-4830	428	26	and	and	CCONJ
ejpam-4830	428	27	it	it	PRON
ejpam-4830	428	28	solves	solve	VERB
ejpam-4830	428	29	the	the	DET
ejpam-4830	428	30	cauchy	cauchy	PROPN
ejpam-4830	428	31	-	-	PUNCT
ejpam-4830	428	32	dirichlet	dirichlet	PROPN
ejpam-4830	428	33	free	free	ADJ
ejpam-4830	428	34	-	-	PUNCT
ejpam-4830	428	35	boundary	boundary	ADJ
ejpam-4830	428	36	problem	problem	NOUN
ejpam-4830	428	37	{	{	PUNCT
ejpam-4830	428	38	lxv	lxv	NOUN
ejpam-4830	428	39	(	(	PUNCT
ejpam-4830	428	40	t	t	PROPN
ejpam-4830	428	41	,	,	PUNCT
ejpam-4830	428	42	x	x	PROPN
ejpam-4830	428	43	,	,	PUNCT
ejpam-4830	428	44	j	j	NOUN
ejpam-4830	428	45	)	)	PUNCT
ejpam-4830	429	1	=	=	SYM
ejpam-4830	429	2	0	0	NUM
ejpam-4830	429	3	,	,	PUNCT
ejpam-4830	429	4	(	(	PUNCT
ejpam-4830	429	5	t	t	PROPN
ejpam-4830	429	6	,	,	PUNCT
ejpam-4830	429	7	x	x	PROPN
ejpam-4830	429	8	,	,	PUNCT
ejpam-4830	429	9	j	j	NOUN
ejpam-4830	429	10	)	)	PUNCT
ejpam-4830	429	11	∈	∈	PROPN
ejpam-4830	430	1	c	c	NOUN
ejpam-4830	430	2	v	v	X
ejpam-4830	430	3	(	(	PUNCT
ejpam-4830	430	4	t	t	PROPN
ejpam-4830	430	5	,	,	PUNCT
ejpam-4830	430	6	x	x	NOUN
ejpam-4830	430	7	,	,	PUNCT
ejpam-4830	430	8	j	j	NOUN
ejpam-4830	430	9	)	)	PUNCT
ejpam-4830	430	10	=	=	SYM
ejpam-4830	430	11	gµc(t	gµc(t	PROPN
ejpam-4830	430	12	,	,	PUNCT
ejpam-4830	430	13	x	x	NOUN
ejpam-4830	430	14	,	,	PUNCT
ejpam-4830	430	15	j	j	PROPN
ejpam-4830	430	16	)	)	PUNCT
ejpam-4830	430	17	,	,	PUNCT
ejpam-4830	430	18	(	(	PUNCT
ejpam-4830	430	19	t	t	PROPN
ejpam-4830	430	20	,	,	PUNCT
ejpam-4830	430	21	x	x	PROPN
ejpam-4830	430	22	,	,	PUNCT
ejpam-4830	430	23	j	j	NOUN
ejpam-4830	430	24	)	)	PUNCT
ejpam-4830	430	25	∈	∈	PROPN
ejpam-4830	431	1	∂c	∂c	PROPN
ejpam-4830	431	2	,	,	PUNCT
ejpam-4830	431	3	(	(	PUNCT
ejpam-4830	431	4	53	53	NUM
ejpam-4830	431	5	)	)	PUNCT
ejpam-4830	431	6	where	where	SCONJ
ejpam-4830	431	7	∂c	∂c	PROPN
ejpam-4830	431	8	is	be	AUX
ejpam-4830	431	9	the	the	DET
ejpam-4830	431	10	boundary	boundary	NOUN
ejpam-4830	431	11	of	of	ADP
ejpam-4830	431	12	the	the	DET
ejpam-4830	431	13	open	open	ADJ
ejpam-4830	431	14	set	set	NOUN
ejpam-4830	431	15	c.	c.	NOUN
ejpam-4830	431	16	by	by	ADP
ejpam-4830	431	17	the	the	DET
ejpam-4830	431	18	local	local	ADJ
ejpam-4830	431	19	time	time	NOUN
ejpam-4830	431	20	space	space	NOUN
ejpam-4830	431	21	formula	formula	NOUN
ejpam-4830	431	22	of	of	ADP
ejpam-4830	431	23	[	[	X
ejpam-4830	431	24	4	4	NUM
ejpam-4830	431	25	]	]	PUNCT
ejpam-4830	431	26	,	,	PUNCT
ejpam-4830	431	27	we	we	PRON
ejpam-4830	431	28	f.	f.	PROPN
ejpam-4830	431	29	sumalpong	sumalpong	PROPN
ejpam-4830	431	30	,	,	PUNCT
ejpam-4830	431	31	m.	m.	PROPN
ejpam-4830	431	32	frondoza	frondoza	PROPN
ejpam-4830	431	33	,	,	PUNCT
ejpam-4830	431	34	n.l	n.l	PROPN
ejpam-4830	431	35	.	.	PROPN
ejpam-4830	431	36	sayson	sayson	PROPN
ejpam-4830	431	37	/	/	SYM
ejpam-4830	431	38	eur	eur	PROPN
ejpam-4830	431	39	.	.	PUNCT
ejpam-4830	432	1	j.	j.	PROPN
ejpam-4830	432	2	pure	pure	PROPN
ejpam-4830	432	3	appl	appl	PROPN
ejpam-4830	432	4	.	.	PROPN
ejpam-4830	432	5	math	math	PROPN
ejpam-4830	432	6	,	,	PUNCT
ejpam-4830	432	7	16	16	NUM
ejpam-4830	432	8	(	(	PUNCT
ejpam-4830	432	9	3	3	NUM
ejpam-4830	432	10	)	)	PUNCT
ejpam-4830	432	11	(	(	PUNCT
ejpam-4830	432	12	2023	2023	NUM
ejpam-4830	432	13	)	)	PUNCT
ejpam-4830	432	14	,	,	PUNCT
ejpam-4830	432	15	1830	1830	NUM
ejpam-4830	432	16	-	-	SYM
ejpam-4830	432	17	1847	1847	NUM
ejpam-4830	432	18	1846	1846	NUM
ejpam-4830	432	19	have	have	VERB
ejpam-4830	432	20	v	v	X
ejpam-4830	432	21	(	(	PUNCT
ejpam-4830	432	22	t	t	PROPN
ejpam-4830	432	23	,	,	PUNCT
ejpam-4830	432	24	xt	xt	PROPN
ejpam-4830	432	25	,	,	PUNCT
ejpam-4830	432	26	j	j	PROPN
ejpam-4830	432	27	)	)	PUNCT
ejpam-4830	432	28	=	=	SYM
ejpam-4830	432	29	e	e	X
ejpam-4830	432	30	[	[	PUNCT
ejpam-4830	432	31	(	(	PUNCT
ejpam-4830	432	32	k	k	NOUN
ejpam-4830	432	33	−xt	−xt	PROPN
ejpam-4830	432	34	)	)	PUNCT
ejpam-4830	433	1	+	+	CCONJ
ejpam-4830	433	2	∣∣∣αt	∣∣∣αt	X
ejpam-4830	433	3	=	=	SYM
ejpam-4830	433	4	j	j	PROPN
ejpam-4830	433	5	,	,	PUNCT
ejpam-4830	433	6	xt	xt	X
ejpam-4830	434	1	=	=	SYM
ejpam-4830	434	2	x	x	X
ejpam-4830	434	3	]	]	X
ejpam-4830	434	4	=	=	SYM
ejpam-4830	434	5	v	v	X
ejpam-4830	434	6	(	(	PUNCT
ejpam-4830	434	7	t	t	PROPN
ejpam-4830	434	8	,	,	PUNCT
ejpam-4830	434	9	x	x	NOUN
ejpam-4830	434	10	,	,	PUNCT
ejpam-4830	434	11	j	j	NOUN
ejpam-4830	434	12	)	)	PUNCT
ejpam-4830	435	1	+	+	NUM
ejpam-4830	435	2	e	e	X
ejpam-4830	435	3	[	[	PUNCT
ejpam-4830	435	4	m	m	PROPN
ejpam-4830	435	5	b	b	NOUN
ejpam-4830	435	6	t	t	NOUN
ejpam-4830	435	7	∣∣∣	∣∣∣	NOUN
ejpam-4830	435	8	αt	αt	PROPN
ejpam-4830	435	9	=	=	SYM
ejpam-4830	435	10	j	j	PROPN
ejpam-4830	435	11	,	,	PUNCT
ejpam-4830	435	12	xt	xt	X
ejpam-4830	436	1	=	=	SYM
ejpam-4830	436	2	x	x	X
ejpam-4830	436	3	]	]	X
ejpam-4830	437	1	+	+	PUNCT
ejpam-4830	437	2	e	e	X
ejpam-4830	437	3	[	[	X
ejpam-4830	437	4	∫	∫	X
ejpam-4830	437	5	t	t	PROPN
ejpam-4830	437	6	t	t	PROPN
ejpam-4830	437	7	lxv	lxv	PROPN
ejpam-4830	437	8	(	(	PUNCT
ejpam-4830	437	9	u	u	NOUN
ejpam-4830	437	10	,	,	PUNCT
ejpam-4830	437	11	xu	xu	PROPN
ejpam-4830	437	12	,	,	PUNCT
ejpam-4830	437	13	αu)i(xu	αu)i(xu	NUM
ejpam-4830	437	14	̸=	̸=	PROPN
ejpam-4830	437	15	bd(u	bd(u	PUNCT
ejpam-4830	437	16	,	,	PUNCT
ejpam-4830	437	17	αu))du	αu))du	PROPN
ejpam-4830	437	18	∣∣∣αt	∣∣∣αt	PROPN
ejpam-4830	437	19	=	=	SYM
ejpam-4830	437	20	j	j	PROPN
ejpam-4830	437	21	,	,	PUNCT
ejpam-4830	437	22	xt	xt	X
ejpam-4830	438	1	=	=	SYM
ejpam-4830	438	2	x	x	X
ejpam-4830	439	1	]	]	X
ejpam-4830	439	2	+	+	CCONJ
ejpam-4830	439	3	1	1	NUM
ejpam-4830	439	4	2	2	NUM
ejpam-4830	439	5	e	e	NOUN
ejpam-4830	439	6	[	[	X
ejpam-4830	439	7	∫	∫	X
ejpam-4830	439	8	t	t	PROPN
ejpam-4830	439	9	t	t	PROPN
ejpam-4830	439	10	(	(	PUNCT
ejpam-4830	439	11	∂v	∂v	PROPN
ejpam-4830	439	12	∂y	∂y	SYM
ejpam-4830	439	13	(	(	PUNCT
ejpam-4830	439	14	u	u	PROPN
ejpam-4830	439	15	,	,	PUNCT
ejpam-4830	439	16	xu+	xu+	PROPN
ejpam-4830	439	17	,	,	PUNCT
ejpam-4830	439	18	αu)−	αu)−	NOUN
ejpam-4830	440	1	∂v	∂v	PROPN
ejpam-4830	440	2	∂y	∂y	SYM
ejpam-4830	440	3	(	(	PUNCT
ejpam-4830	440	4	u	u	NOUN
ejpam-4830	440	5	,	,	PUNCT
ejpam-4830	440	6	xu−	xu−	PROPN
ejpam-4830	440	7	,	,	PUNCT
ejpam-4830	440	8	αu	αu	NOUN
ejpam-4830	440	9	)	)	PUNCT
ejpam-4830	440	10	)	)	PUNCT
ejpam-4830	440	11	i(xu	i(xu	PROPN
ejpam-4830	440	12	=	=	SYM
ejpam-4830	440	13	bd(u	bd(u	X
ejpam-4830	440	14	,	,	PUNCT
ejpam-4830	440	15	αu)dℓ	αu)dℓ	X
ejpam-4830	440	16	b	b	X
ejpam-4830	440	17	u(x	u(x	X
ejpam-4830	440	18	x	x	X
ejpam-4830	440	19	)	)	PUNCT
ejpam-4830	440	20	∣∣∣αt	∣∣∣αt	X
ejpam-4830	440	21	=	=	SYM
ejpam-4830	440	22	j	j	PROPN
ejpam-4830	440	23	,	,	PUNCT
ejpam-4830	440	24	xt	xt	X
ejpam-4830	440	25	=	=	SYM
ejpam-4830	440	26	x	x	SYM
ejpam-4830	440	27	]	]	X
ejpam-4830	440	28	(	(	PUNCT
ejpam-4830	440	29	54	54	NUM
ejpam-4830	440	30	)	)	PUNCT
ejpam-4830	440	31	wherem	wherem	PROPN
ejpam-4830	440	32	b	b	PROPN
ejpam-4830	440	33	t	t	PROPN
ejpam-4830	440	34	=	=	SYM
ejpam-4830	440	35	∫	∫	PROPN
ejpam-4830	440	36	t	t	PROPN
ejpam-4830	440	37	t	t	PROPN
ejpam-4830	440	38	σ(αu)xu	σ(αu)xu	NOUN
ejpam-4830	440	39	∂v	∂v	PROPN
ejpam-4830	440	40	∂x	∂x	PROPN
ejpam-4830	440	41	dwu	dwu	PROPN
ejpam-4830	440	42	is	be	AUX
ejpam-4830	440	43	a	a	DET
ejpam-4830	440	44	continuous	continuous	ADJ
ejpam-4830	440	45	local	local	ADJ
ejpam-4830	440	46	martingale	martingale	NOUN
ejpam-4830	440	47	and	and	CCONJ
ejpam-4830	440	48	ℓb	ℓb	NOUN
ejpam-4830	440	49	=	=	PUNCT
ejpam-4830	440	50	(	(	PUNCT
ejpam-4830	440	51	ℓbu(x	ℓbu(x	X
ejpam-4830	440	52	x))t≤u≤t	x))t≤u≤t	PRON
ejpam-4830	440	53	is	be	AUX
ejpam-4830	440	54	the	the	DET
ejpam-4830	440	55	local	local	ADJ
ejpam-4830	440	56	time	time	NOUN
ejpam-4830	440	57	of	of	ADP
ejpam-4830	440	58	xx	xx	NUM
ejpam-4830	440	59	=	=	SYM
ejpam-4830	440	60	(	(	PUNCT
ejpam-4830	440	61	xu)t≤u≤t	xu)t≤u≤t	PROPN
ejpam-4830	440	62	at	at	ADP
ejpam-4830	440	63	the	the	DET
ejpam-4830	440	64	curve	curve	NOUN
ejpam-4830	440	65	u	u	PROPN
ejpam-4830	440	66	7→	7→	PROPN
ejpam-4830	440	67	bd(u	bd(u	PUNCT
ejpam-4830	440	68	,	,	PUNCT
ejpam-4830	440	69	j	j	PROPN
ejpam-4830	440	70	)	)	PUNCT
ejpam-4830	440	71	.	.	PUNCT
ejpam-4830	441	1	using	use	VERB
ejpam-4830	441	2	that	that	SCONJ
ejpam-4830	441	3	∂gµc	∂gµc	ADJ
ejpam-4830	441	4	∂x	∂x	PROPN
ejpam-4830	441	5	(	(	PUNCT
ejpam-4830	441	6	t	t	PROPN
ejpam-4830	441	7	,	,	PUNCT
ejpam-4830	441	8	x	x	PROPN
ejpam-4830	441	9	,	,	PUNCT
ejpam-4830	441	10	j	j	NOUN
ejpam-4830	441	11	)	)	PUNCT
ejpam-4830	441	12	=	=	SYM
ejpam-4830	441	13	−p(x	−p(x	NOUN
ejpam-4830	441	14	≤	≤	NUM
ejpam-4830	441	15	k	k	NOUN
ejpam-4830	441	16	)	)	PUNCT
ejpam-4830	441	17	≤	≤	PUNCT
ejpam-4830	442	1	∂v	∂v	PROPN
ejpam-4830	442	2	∂x	∂x	PROPN
ejpam-4830	442	3	(	(	PUNCT
ejpam-4830	442	4	t	t	PROPN
ejpam-4830	442	5	,	,	PUNCT
ejpam-4830	442	6	y	y	PROPN
ejpam-4830	442	7	,	,	PUNCT
ejpam-4830	442	8	j	j	NOUN
ejpam-4830	442	9	)	)	PUNCT
ejpam-4830	442	10	≤	≤	NOUN
ejpam-4830	442	11	0	0	NUM
ejpam-4830	443	1	for	for	ADP
ejpam-4830	443	2	all	all	DET
ejpam-4830	443	3	t	t	NOUN
ejpam-4830	443	4	∈	∈	PROPN
ejpam-4830	444	1	[	[	X
ejpam-4830	444	2	0	0	NUM
ejpam-4830	444	3	,	,	PUNCT
ejpam-4830	444	4	t	t	NOUN
ejpam-4830	444	5	)	)	PUNCT
ejpam-4830	444	6	,	,	PUNCT
ejpam-4830	444	7	it	it	PRON
ejpam-4830	444	8	can	can	AUX
ejpam-4830	444	9	easily	easily	ADV
ejpam-4830	444	10	be	be	AUX
ejpam-4830	444	11	verified	verify	VERB
ejpam-4830	444	12	from	from	ADP
ejpam-4830	444	13	proposition	proposition	NOUN
ejpam-4830	444	14	4.4	4.4	NUM
ejpam-4830	444	15	,	,	PUNCT
ejpam-4830	444	16	page	page	NOUN
ejpam-4830	444	17	45	45	NUM
ejpam-4830	444	18	in	in	ADP
ejpam-4830	444	19	[	[	X
ejpam-4830	444	20	1	1	X
ejpam-4830	444	21	]	]	PUNCT
ejpam-4830	444	22	that	that	SCONJ
ejpam-4830	444	23	e	e	X
ejpam-4830	444	24	[	[	PUNCT
ejpam-4830	444	25	m	m	PROPN
ejpam-4830	444	26	b	b	X
ejpam-4830	444	27	t	t	NOUN
ejpam-4830	444	28	]	]	PUNCT
ejpam-4830	445	1	=	=	PUNCT
ejpam-4830	445	2	0	0	X
ejpam-4830	445	3	.	.	PUNCT
ejpam-4830	446	1	by	by	ADP
ejpam-4830	446	2	the	the	DET
ejpam-4830	446	3	smooth	smooth	ADJ
ejpam-4830	446	4	-	-	PUNCT
ejpam-4830	446	5	fit	fit	NOUN
ejpam-4830	446	6	property	property	NOUN
ejpam-4830	446	7	shown	show	VERB
ejpam-4830	446	8	in	in	ADP
ejpam-4830	446	9	lemma	lemma	PROPN
ejpam-4830	446	10	7	7	NUM
ejpam-4830	446	11	,	,	PUNCT
ejpam-4830	446	12	the	the	DET
ejpam-4830	446	13	last	last	ADJ
ejpam-4830	446	14	two	two	NUM
ejpam-4830	446	15	terms	term	NOUN
ejpam-4830	446	16	in	in	ADP
ejpam-4830	446	17	(	(	PUNCT
ejpam-4830	446	18	54	54	NUM
ejpam-4830	446	19	)	)	PUNCT
ejpam-4830	446	20	above	above	ADP
ejpam-4830	446	21	vanishes	vanishe	NOUN
ejpam-4830	446	22	.	.	PUNCT
ejpam-4830	447	1	furthermore	furthermore	ADV
ejpam-4830	447	2	,	,	PUNCT
ejpam-4830	447	3	by	by	ADP
ejpam-4830	447	4	(	(	PUNCT
ejpam-4830	447	5	53	53	NUM
ejpam-4830	447	6	)	)	PUNCT
ejpam-4830	447	7	above	above	ADV
ejpam-4830	447	8	and	and	CCONJ
ejpam-4830	447	9	the	the	DET
ejpam-4830	447	10	fact	fact	NOUN
ejpam-4830	447	11	that	that	SCONJ
ejpam-4830	447	12	v	v	X
ejpam-4830	447	13	=	=	NOUN
ejpam-4830	447	14	gµc	gµc	NOUN
ejpam-4830	447	15	in	in	ADP
ejpam-4830	447	16	the	the	DET
ejpam-4830	447	17	closed	closed	ADJ
ejpam-4830	447	18	set	set	NOUN
ejpam-4830	447	19	d	d	NOUN
ejpam-4830	447	20	,	,	PUNCT
ejpam-4830	447	21	equation	equation	NOUN
ejpam-4830	447	22	(	(	PUNCT
ejpam-4830	447	23	54	54	NUM
ejpam-4830	447	24	)	)	PUNCT
ejpam-4830	447	25	becomes	become	VERB
ejpam-4830	447	26	e	e	NOUN
ejpam-4830	447	27	[	[	PUNCT
ejpam-4830	447	28	(	(	PUNCT
ejpam-4830	447	29	k	k	NOUN
ejpam-4830	447	30	−xt	−xt	PROPN
ejpam-4830	447	31	)	)	PUNCT
ejpam-4830	447	32	+	+	CCONJ
ejpam-4830	447	33	∣∣∣αt	∣∣∣αt	X
ejpam-4830	447	34	=	=	SYM
ejpam-4830	447	35	j	j	PROPN
ejpam-4830	447	36	,	,	PUNCT
ejpam-4830	447	37	xt	xt	X
ejpam-4830	447	38	=	=	SYM
ejpam-4830	447	39	x	x	X
ejpam-4830	447	40	]	]	X
ejpam-4830	447	41	=	=	SYM
ejpam-4830	447	42	gµc(t	gµc(t	PROPN
ejpam-4830	447	43	,	,	PUNCT
ejpam-4830	447	44	x	x	NOUN
ejpam-4830	447	45	,	,	PUNCT
ejpam-4830	447	46	j	j	PROPN
ejpam-4830	447	47	)	)	PUNCT
ejpam-4830	448	1	+	+	CCONJ
ejpam-4830	448	2	∫	∫	PROPN
ejpam-4830	448	3	t	t	PROPN
ejpam-4830	448	4	t	t	X
ejpam-4830	448	5	e	e	X
ejpam-4830	448	6	[	[	PUNCT
ejpam-4830	448	7	lxv	lxv	NOUN
ejpam-4830	448	8	(	(	PUNCT
ejpam-4830	448	9	u	u	NOUN
ejpam-4830	448	10	,	,	PUNCT
ejpam-4830	448	11	xu	xu	PROPN
ejpam-4830	448	12	,	,	PUNCT
ejpam-4830	448	13	αu)i(xu	αu)i(xu	X
ejpam-4830	448	14	<	<	X
ejpam-4830	448	15	bd(u	bd(u	PROPN
ejpam-4830	448	16	,	,	PUNCT
ejpam-4830	448	17	αu	αu	NOUN
ejpam-4830	448	18	)	)	PUNCT
ejpam-4830	448	19	)	)	PUNCT
ejpam-4830	449	1	∣∣∣αt	∣∣∣αt	X
ejpam-4830	449	2	=	=	SYM
ejpam-4830	449	3	j	j	PROPN
ejpam-4830	449	4	,	,	PUNCT
ejpam-4830	449	5	xt	xt	X
ejpam-4830	450	1	=	=	SYM
ejpam-4830	450	2	x	x	X
ejpam-4830	450	3	]	]	X
ejpam-4830	450	4	du	du	X
ejpam-4830	450	5	.	.	X
ejpam-4830	451	1	(	(	PUNCT
ejpam-4830	451	2	55	55	NUM
ejpam-4830	451	3	)	)	PUNCT
ejpam-4830	451	4	substituting	substitute	VERB
ejpam-4830	451	5	x	x	PUNCT
ejpam-4830	451	6	with	with	ADP
ejpam-4830	451	7	bd(t	bd(t	PROPN
ejpam-4830	451	8	,	,	PUNCT
ejpam-4830	451	9	j	j	PROPN
ejpam-4830	451	10	)	)	PUNCT
ejpam-4830	451	11	,	,	PUNCT
ejpam-4830	451	12	we	we	PRON
ejpam-4830	451	13	have	have	VERB
ejpam-4830	451	14	gµc(t	gµc(t	NOUN
ejpam-4830	451	15	,	,	PUNCT
ejpam-4830	451	16	bd(t	bd(t	NOUN
ejpam-4830	451	17	,	,	PUNCT
ejpam-4830	451	18	j	j	PROPN
ejpam-4830	451	19	)	)	PUNCT
ejpam-4830	451	20	,	,	PUNCT
ejpam-4830	451	21	j	j	NOUN
ejpam-4830	451	22	)	)	PUNCT
ejpam-4830	451	23	=	=	SYM
ejpam-4830	451	24	e	e	X
ejpam-4830	451	25	[	[	PUNCT
ejpam-4830	451	26	(	(	PUNCT
ejpam-4830	451	27	k	k	NOUN
ejpam-4830	451	28	−xt	−xt	PROPN
ejpam-4830	451	29	)	)	PUNCT
ejpam-4830	452	1	+	+	CCONJ
ejpam-4830	452	2	∣∣∣αt	∣∣∣αt	X
ejpam-4830	452	3	=	=	SYM
ejpam-4830	452	4	j	j	PROPN
ejpam-4830	452	5	,	,	PUNCT
ejpam-4830	452	6	xt	xt	X
ejpam-4830	452	7	=	=	SYM
ejpam-4830	452	8	bd(t	bd(t	PROPN
ejpam-4830	452	9	,	,	PUNCT
ejpam-4830	452	10	j	j	PROPN
ejpam-4830	452	11	)	)	PUNCT
ejpam-4830	452	12	]	]	PUNCT
ejpam-4830	453	1	−	−	PROPN
ejpam-4830	453	2	∫	∫	PROPN
ejpam-4830	453	3	t	t	PROPN
ejpam-4830	453	4	t	t	X
ejpam-4830	453	5	e	e	X
ejpam-4830	453	6	[	[	PUNCT
ejpam-4830	453	7	lxv	lxv	NOUN
ejpam-4830	453	8	(	(	PUNCT
ejpam-4830	453	9	u	u	NOUN
ejpam-4830	453	10	,	,	PUNCT
ejpam-4830	453	11	xu	xu	PROPN
ejpam-4830	453	12	,	,	PUNCT
ejpam-4830	453	13	αu)i(xu	αu)i(xu	X
ejpam-4830	453	14	<	<	X
ejpam-4830	453	15	bd(u	bd(u	PROPN
ejpam-4830	453	16	,	,	PUNCT
ejpam-4830	453	17	αu	αu	NOUN
ejpam-4830	453	18	)	)	PUNCT
ejpam-4830	453	19	)	)	PUNCT
ejpam-4830	453	20	∣∣∣αt	∣∣∣αt	X
ejpam-4830	454	1	=	=	SYM
ejpam-4830	454	2	j	j	PROPN
ejpam-4830	454	3	,	,	PUNCT
ejpam-4830	454	4	xt	xt	X
ejpam-4830	454	5	=	=	SYM
ejpam-4830	454	6	bd(t	bd(t	PROPN
ejpam-4830	454	7	,	,	PUNCT
ejpam-4830	454	8	j	j	NOUN
ejpam-4830	454	9	)	)	PUNCT
ejpam-4830	454	10	]	]	PUNCT
ejpam-4830	455	1	du	du	PROPN
ejpam-4830	455	2	=	=	SYM
ejpam-4830	455	3	f	f	PROPN
ejpam-4830	455	4	(	(	PUNCT
ejpam-4830	455	5	t	t	PROPN
ejpam-4830	455	6	,	,	PUNCT
ejpam-4830	455	7	bd(t	bd(t	PROPN
ejpam-4830	455	8	,	,	PUNCT
ejpam-4830	455	9	j	j	NOUN
ejpam-4830	455	10	)	)	PUNCT
ejpam-4830	455	11	,	,	PUNCT
ejpam-4830	455	12	j)−	j)−	PROPN
ejpam-4830	455	13	∫	∫	PROPN
ejpam-4830	455	14	t	t	PROPN
ejpam-4830	455	15	t	t	PROPN
ejpam-4830	455	16	j(t	j(t	PROPN
ejpam-4830	455	17	,	,	PUNCT
ejpam-4830	455	18	bd(t	bd(t	PROPN
ejpam-4830	455	19	,	,	PUNCT
ejpam-4830	455	20	j	j	PROPN
ejpam-4830	455	21	)	)	PUNCT
ejpam-4830	455	22	,	,	PUNCT
ejpam-4830	455	23	u	u	NOUN
ejpam-4830	455	24	,	,	PUNCT
ejpam-4830	455	25	bd(u	bd(u	X
ejpam-4830	455	26	,	,	PUNCT
ejpam-4830	455	27	αu	αu	NOUN
ejpam-4830	455	28	)	)	PUNCT
ejpam-4830	455	29	,	,	PUNCT
ejpam-4830	455	30	αu	αu	NOUN
ejpam-4830	455	31	)	)	PUNCT
ejpam-4830	455	32	.	.	PUNCT
ejpam-4830	456	1	4	4	X
ejpam-4830	456	2	.	.	X
ejpam-4830	456	3	conclusion	conclusion	NOUN
ejpam-4830	456	4	and	and	CCONJ
ejpam-4830	456	5	recommendations	recommendation	NOUN
ejpam-4830	456	6	this	this	DET
ejpam-4830	456	7	paper	paper	NOUN
ejpam-4830	456	8	extends	extend	VERB
ejpam-4830	456	9	the	the	DET
ejpam-4830	456	10	results	result	NOUN
ejpam-4830	456	11	for	for	ADP
ejpam-4830	456	12	british	british	ADJ
ejpam-4830	456	13	put	put	NOUN
ejpam-4830	456	14	option	option	NOUN
ejpam-4830	456	15	that	that	PRON
ejpam-4830	456	16	was	be	AUX
ejpam-4830	456	17	introduced	introduce	VERB
ejpam-4830	456	18	by	by	ADP
ejpam-4830	456	19	g.	g.	PROPN
ejpam-4830	456	20	peskir	peskir	PROPN
ejpam-4830	456	21	and	and	CCONJ
ejpam-4830	456	22	f.	f.	PROPN
ejpam-4830	456	23	samee	samee	PROPN
ejpam-4830	456	24	(	(	PUNCT
ejpam-4830	456	25	2011	2011	NUM
ejpam-4830	456	26	)	)	PUNCT
ejpam-4830	456	27	by	by	ADP
ejpam-4830	456	28	considering	consider	VERB
ejpam-4830	456	29	stochastic	stochastic	ADJ
ejpam-4830	456	30	volatility	volatility	NOUN
ejpam-4830	456	31	,	,	PUNCT
ejpam-4830	456	32	particularly	particularly	ADV
ejpam-4830	456	33	in	in	ADP
ejpam-4830	456	34	a	a	DET
ejpam-4830	456	35	regime	regime	NOUN
ejpam-4830	456	36	-	-	PUNCT
ejpam-4830	456	37	switching	switching	NOUN
ejpam-4830	456	38	.	.	PUNCT
ejpam-4830	457	1	we	we	PRON
ejpam-4830	457	2	have	have	AUX
ejpam-4830	457	3	shown	show	VERB
ejpam-4830	457	4	that	that	SCONJ
ejpam-4830	457	5	the	the	DET
ejpam-4830	457	6	boundary	boundary	ADJ
ejpam-4830	457	7	function	function	NOUN
ejpam-4830	457	8	satisfies	satisfy	VERB
ejpam-4830	457	9	the	the	DET
ejpam-4830	457	10	volterra	volterra	NOUN
ejpam-4830	457	11	equation	equation	NOUN
ejpam-4830	457	12	,	,	PUNCT
ejpam-4830	457	13	instead	instead	ADV
ejpam-4830	457	14	of	of	ADP
ejpam-4830	457	15	deriving	derive	VERB
ejpam-4830	457	16	the	the	DET
ejpam-4830	457	17	closed	closed	ADJ
ejpam-4830	457	18	form	form	NOUN
ejpam-4830	457	19	expression	expression	NOUN
ejpam-4830	457	20	for	for	ADP
ejpam-4830	457	21	the	the	DET
ejpam-4830	457	22	arbitrage	arbitrage	NOUN
ejpam-4830	457	23	-	-	PUNCT
ejpam-4830	457	24	free	free	ADJ
ejpam-4830	457	25	price	price	NOUN
ejpam-4830	457	26	for	for	ADP
ejpam-4830	457	27	the	the	DET
ejpam-4830	457	28	british	british	ADJ
ejpam-4830	457	29	put	put	NOUN
ejpam-4830	457	30	option	option	NOUN
ejpam-4830	457	31	.	.	PUNCT
ejpam-4830	458	1	for	for	ADP
ejpam-4830	458	2	further	further	ADJ
ejpam-4830	458	3	studies	study	NOUN
ejpam-4830	458	4	,	,	PUNCT
ejpam-4830	458	5	a	a	DET
ejpam-4830	458	6	similar	similar	ADJ
ejpam-4830	458	7	extension	extension	NOUN
ejpam-4830	458	8	may	may	AUX
ejpam-4830	458	9	be	be	AUX
ejpam-4830	458	10	done	do	VERB
ejpam-4830	458	11	for	for	ADP
ejpam-4830	458	12	the	the	DET
ejpam-4830	458	13	british	british	ADJ
ejpam-4830	458	14	call	call	NOUN
ejpam-4830	458	15	option	option	NOUN
ejpam-4830	458	16	.	.	PUNCT
ejpam-4830	459	1	in	in	ADP
ejpam-4830	459	2	addition	addition	NOUN
ejpam-4830	459	3	,	,	PUNCT
ejpam-4830	459	4	references	reference	NOUN
ejpam-4830	459	5	1847	1847	NUM
ejpam-4830	459	6	one	one	NUM
ejpam-4830	459	7	may	may	AUX
ejpam-4830	459	8	provide	provide	VERB
ejpam-4830	459	9	a	a	DET
ejpam-4830	459	10	practical	practical	ADJ
ejpam-4830	459	11	implication	implication	NOUN
ejpam-4830	459	12	of	of	ADP
ejpam-4830	459	13	this	this	DET
ejpam-4830	459	14	study	study	NOUN
ejpam-4830	459	15	.	.	PUNCT
ejpam-4830	460	1	references	reference	NOUN
ejpam-4830	460	2	[	[	X
ejpam-4830	460	3	1	1	NUM
ejpam-4830	460	4	]	]	PUNCT
ejpam-4830	460	5	t	t	PROPN
ejpam-4830	460	6	björk	björk	PROPN
ejpam-4830	460	7	.	.	PUNCT
ejpam-4830	461	1	arbitrage	arbitrage	NOUN
ejpam-4830	461	2	theory	theory	NOUN
ejpam-4830	461	3	in	in	ADP
ejpam-4830	461	4	continuous	continuous	ADJ
ejpam-4830	461	5	time	time	NOUN
ejpam-4830	461	6	.	.	PUNCT
ejpam-4830	462	1	oxford	oxford	PROPN
ejpam-4830	462	2	university	university	PROPN
ejpam-4830	462	3	press	press	NOUN
ejpam-4830	462	4	,	,	PUNCT
ejpam-4830	462	5	new	new	PROPN
ejpam-4830	462	6	york	york	PROPN
ejpam-4830	462	7	,	,	PUNCT
ejpam-4830	462	8	2009	2009	NUM
ejpam-4830	462	9	.	.	PUNCT
ejpam-4830	463	1	[	[	X
ejpam-4830	463	2	2	2	X
ejpam-4830	463	3	]	]	X
ejpam-4830	463	4	q	q	X
ejpam-4830	463	5	zhang	zhang	PROPN
ejpam-4830	463	6	d	d	X
ejpam-4830	463	7	yao	yao	PROPN
ejpam-4830	463	8	and	and	CCONJ
ejpam-4830	463	9	x	x	X
ejpam-4830	463	10	y	y	PROPN
ejpam-4830	463	11	zhou	zhou	PROPN
ejpam-4830	463	12	.	.	PUNCT
ejpam-4830	464	1	a	a	DET
ejpam-4830	464	2	regime	regime	NOUN
ejpam-4830	464	3	-	-	PUNCT
ejpam-4830	464	4	switching	switching	NOUN
ejpam-4830	464	5	for	for	ADP
ejpam-4830	464	6	european	european	ADJ
ejpam-4830	464	7	options	option	NOUN
ejpam-4830	464	8	.	.	PUNCT
ejpam-4830	465	1	international	international	ADJ
ejpam-4830	465	2	series	series	PROPN
ejpam-4830	465	3	in	in	ADP
ejpam-4830	465	4	operation	operation	NOUN
ejpam-4830	465	5	research	research	NOUN
ejpam-4830	465	6	and	and	CCONJ
ejpam-4830	465	7	management	management	NOUN
ejpam-4830	465	8	science	science	NOUN
ejpam-4830	465	9	,	,	PUNCT
ejpam-4830	465	10	94:281–300	94:281–300	NUM
ejpam-4830	465	11	,	,	PUNCT
ejpam-4830	465	12	2006	2006	NUM
ejpam-4830	465	13	.	.	PUNCT
ejpam-4830	466	1	[	[	X
ejpam-4830	466	2	3	3	X
ejpam-4830	466	3	]	]	PUNCT
ejpam-4830	466	4	a	a	DET
ejpam-4830	466	5	i	i	PROPN
ejpam-4830	466	6	khuri	khuri	PROPN
ejpam-4830	466	7	.	.	PUNCT
ejpam-4830	467	1	advanced	advanced	ADJ
ejpam-4830	467	2	calculus	calculus	NOUN
ejpam-4830	467	3	with	with	ADP
ejpam-4830	467	4	applications	application	NOUN
ejpam-4830	467	5	in	in	ADP
ejpam-4830	467	6	statistics	statistic	NOUN
ejpam-4830	467	7	(	(	PUNCT
ejpam-4830	467	8	2nd	2nd	ADJ
ejpam-4830	467	9	ed	ed	NOUN
ejpam-4830	467	10	.	.	PUNCT
ejpam-4830	467	11	)	)	PUNCT
ejpam-4830	467	12	.	.	PUNCT
ejpam-4830	468	1	john	john	PROPN
ejpam-4830	468	2	wiley	wiley	PROPN
ejpam-4830	468	3	and	and	CCONJ
ejpam-4830	468	4	sons	son	NOUN
ejpam-4830	468	5	,	,	PUNCT
ejpam-4830	468	6	new	new	PROPN
ejpam-4830	468	7	york	york	PROPN
ejpam-4830	468	8	,	,	PUNCT
ejpam-4830	468	9	2003	2003	NUM
ejpam-4830	468	10	.	.	PUNCT
ejpam-4830	469	1	[	[	X
ejpam-4830	469	2	4	4	X
ejpam-4830	469	3	]	]	X
ejpam-4830	469	4	g	g	NOUN
ejpam-4830	469	5	peskir	peskir	NOUN
ejpam-4830	469	6	.	.	PUNCT
ejpam-4830	470	1	a	a	DET
ejpam-4830	470	2	change	change	NOUN
ejpam-4830	470	3	-	-	PUNCT
ejpam-4830	470	4	of	of	ADP
ejpam-4830	470	5	-	-	PUNCT
ejpam-4830	470	6	variable	variable	ADJ
ejpam-4830	470	7	formula	formula	NOUN
ejpam-4830	470	8	with	with	ADP
ejpam-4830	470	9	local	local	ADJ
ejpam-4830	470	10	time	time	NOUN
ejpam-4830	470	11	on	on	ADP
ejpam-4830	470	12	curves	curve	NOUN
ejpam-4830	470	13	.	.	PUNCT
ejpam-4830	471	1	journal	journal	NOUN
ejpam-4830	471	2	of	of	ADP
ejpam-4830	471	3	theoretical	theoretical	ADJ
ejpam-4830	471	4	probability	probability	NOUN
ejpam-4830	471	5	,	,	PUNCT
ejpam-4830	471	6	3:499–535	3:499–535	PROPN
ejpam-4830	471	7	,	,	PUNCT
ejpam-4830	471	8	2005	2005	NUM
ejpam-4830	471	9	.	.	PUNCT
ejpam-4830	472	1	[	[	X
ejpam-4830	472	2	5	5	X
ejpam-4830	472	3	]	]	PUNCT
ejpam-4830	472	4	g	g	NOUN
ejpam-4830	472	5	peskir	peskir	NOUN
ejpam-4830	472	6	and	and	CCONJ
ejpam-4830	472	7	f	f	PROPN
ejpam-4830	472	8	samee	samee	PROPN
ejpam-4830	472	9	.	.	PUNCT
ejpam-4830	473	1	the	the	DET
ejpam-4830	473	2	british	british	ADJ
ejpam-4830	473	3	put	put	VERB
ejpam-4830	473	4	option	option	NOUN
ejpam-4830	473	5	.	.	PUNCT
ejpam-4830	474	1	journal	journal	NOUN
ejpam-4830	474	2	of	of	ADP
ejpam-4830	474	3	theoretical	theoretical	ADJ
ejpam-4830	474	4	probability	probability	NOUN
ejpam-4830	474	5	,	,	PUNCT
ejpam-4830	474	6	6:537–563	6:537–563	NOUN
ejpam-4830	474	7	,	,	PUNCT
ejpam-4830	474	8	2011	2011	NUM
ejpam-4830	474	9	.	.	PUNCT
ejpam-4830	475	1	[	[	X
ejpam-4830	475	2	6	6	NUM
ejpam-4830	475	3	]	]	PUNCT
ejpam-4830	475	4	g	g	NOUN
ejpam-4830	475	5	peskir	peskir	NOUN
ejpam-4830	475	6	and	and	CCONJ
ejpam-4830	475	7	a	a	DET
ejpam-4830	475	8	shiryaev	shiryaev	NOUN
ejpam-4830	475	9	.	.	PUNCT
ejpam-4830	475	10	optimal	optimal	ADJ
ejpam-4830	475	11	stopping	stopping	NOUN
ejpam-4830	475	12	and	and	CCONJ
ejpam-4830	475	13	free	free	ADJ
ejpam-4830	475	14	-	-	PUNCT
ejpam-4830	475	15	boundary	boundary	NOUN
ejpam-4830	475	16	problems	problem	NOUN
ejpam-4830	475	17	.	.	PUNCT
ejpam-4830	476	1	lectures	lecture	NOUN
ejpam-4830	476	2	in	in	ADP
ejpam-4830	476	3	mathematics	mathematics	PROPN
ejpam-4830	476	4	eth	eth	PROPN
ejpam-4830	476	5	zürich	zürich	PROPN
ejpam-4830	476	6	.	.	PROPN
ejpam-4830	476	7	,	,	PUNCT
ejpam-4830	476	8	birkhäuser	birkhäuser	X
ejpam-4830	476	9	verlag	verlag	PROPN
ejpam-4830	476	10	,	,	PUNCT
ejpam-4830	476	11	berlag	berlag	NOUN
ejpam-4830	476	12	,	,	PUNCT
ejpam-4830	476	13	2006	2006	NUM
ejpam-4830	476	14	.	.	PUNCT